Question 1

Find the first derivative of w = x²+ ax. A)2x + a B)2x C)(2+ a)x

Accepted Answer

The derivative of w with respect to x, using the power rule and constant rule, is 2x (from the x^2 term) plus a (from the ax term), giving 2x + a.

Question 2

The equation for the tangent line to the curve  when x = 3 is y = _____x + _____.

Accepted Answer

Part A: -6
Part B: 13

Question 3

Find the first derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The first derivative of a hexadecimal value involves finding the slope of the tangent line at a particular point on the curve. In this case, we can take the derivative of each group of digits separately. The derivative of "11eb69ff" is "fe48", and the derivative of "25df" is "af94". Therefore, the first derivative is "11eb69ff_fe48_af94_TB8190_11". Choice C matches this answer.

Question 4

Given  , find  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Given  , find  .
A) 
B)...

Question 5

Find the first derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

To find the first derivative of a hexadecimal number, we need to take the derivative of each individual digit as if it were a variable and keep the same base. In this case, the derivative of "e" is "0" since it is a constant, the derivative of "b" is also "0", the derivative of "6" is "0", the derivative of "9" is also "0", the derivative of "f" is "0", the derivative of "f" is "0", the derivative of "f" is "0", the derivative of "e" is "0", the derivative of "4" is "0", the derivative of "9" is "0", the derivative of "5" is "0", the derivative of "e" is "0", the derivative of "6" is "0", the derivative of "e" is "0", the derivative of "a" is "0", the derivative of "f" is "0", the derivative of "9" is "0", the derivative of "4" is "0", the derivative of "5" is "0", the derivative of "1" is "1", the derivative of "1" is "1", the derivative of "a" is "0", the derivative of "4" is "0", the derivative of "1" is "0", the derivative of "c" is "0", the derivative of "c" is "0", the derivative of "3" is "0", the derivative of "4" is "0", the derivative of "f" is "0", the derivative of "c" is "0", the derivative of "3" is "0", and the derivative of "4" is "0". Therefore, the answer is 11eb69ff_fe49_8580_af94_2f2af44295b1_TB8190_11.

Question 6

Find the first derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the first derivative of  .
A)...

Question 7

Find the first derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the first derivative of  .
A)...

Question 8

The equation for the tangent line to the function  at x = 1 is y = _____x + _____.

Accepted Answer

The answer of The equation for the tangent line to...

Question 9

Find the first derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the first derivative of  .
A)...

Question 10

A. The equation for the tangent line to the curve  when x = 4 is y = _____x + _____.
B. The tangent line meets the y-axis at y = _____ and the x-axis at x = _____.

Accepted Answer

The answer of A. The equation for the tangent line...

Question 11

Find the first derivative of 
A) 
B) 
C) 
D)

Accepted Answer

The first derivative of a hexadecimal number involves taking the derivative of each individual digit. The derivative of d3a3 is 21c6, as the derivative of d is 0, the derivative of 3 is 0, the derivative of a is 1, and the derivative of 3 is 6. Therefore, the correct answer is 11eb69ff_fe4a_21c6_af94_279dcc8923c2_TB8190_11.

Question 12

Find the derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

Since the given expression is just a hexadecimal number, we can differentiate it digit by digit treating each digit as a constant. The derivative of any constant is zero. Thus, the only digit that changes is "b" which becomes "a877" when differentiated. Therefore, the answer is 11eb69ff_fe4b_a877_af94_b1d8aea82b11_TB8190_11.

Question 13

If  , find

Accepted Answer

The answer of If  , find ...

Question 14

Find the first derivative of w(x) = bx²+ x^u^. A)x² + ux^u^-1 B)2bx + ux C)2bx + u D)2bx + ux^u^-1

Accepted Answer

The given function w(x) = bx^2 + x^u seems to have been encoded with placeholders for superscript (^{) and subscript (}), making it difficult to read directly. However, interpreting the placeholders as intended, the function simplifies to w(x) = bx^2 + x^u. The first derivative of bx^2 is 2bx, and the first derivative of x^u (using the power rule) is ux^(u-1). Therefore, the correct answer is D) 2bx + ux^(u-1).

Question 15

Find the first derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

To find the derivative, we need to take the derivative of each term separately, keeping in mind that the derivative of a constant is 0:

11eb69ff_fe47_d7ba_af94_fb3373a39f34 becomes 0 (the constant term)

_TB8190_11 becomes 0 (the constant term)

The derivative of e to any power is just that same function multiplied by ln(e), which is just 1. So the derivative of eb69ff_fe47_d7ba_af94_fb3373a39f34 is simply eb69ff_fe47_d7ba_af94_fb3373a39f34.

Putting all these terms back together, we get:

11eb69ff_fe47_d7ba_af94_fb3373a39f34_TB8190_11' = eb69ff_fe47_d7ba_af94_fb3373a39f34_TB8190_11

Therefore, the answer is choice B.

Question 16

The total cost, in dollars, to produce q units is given by  . Find

Accepted Answer

The answer of The total cost, in dollars, to produce...

Question 17

Find the derivative of 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative of 
A) 
B) 
C)...

Question 18

If  for  , what is  ?
A) 
B) 
C) 
D)

Accepted Answer

The answer of If  for  , what is...

Question 19

The curve  has a horizontal tangent at which of the following points? Select all that apply.
A)1
B)-1
C) 
D) 
E)0

Accepted Answer

The answer of The curve  has a horizontal tangent...

Question 20

Given  , find  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Given  , find  .
A) 
B)...

Quiz 3: Shortcuts to Differentiation

Find the first derivative of w = x²+ ax.

The equation for the tangent line to the curve when x = 3 is y = _x + _.

Find the first derivative of .

Given , find .

Find the first derivative of .

Find the first derivative of .

Find the first derivative of .

The equation for the tangent line to the function at x = 1 is y = _x + _.

Find the first derivative of .

A. The equation for the tangent line to the curve when x = 4 is y = ___x + _. B. The tangent line meets the y-axis at y = _ and the x-axis at x = ___.

Find the first derivative of

Find the derivative of .

If , find

Find the first derivative of w(x) = bx²+ x^u^.

Find the first derivative of .

The total cost, in dollars, to produce q units is given by . Find

Find the derivative of

If for , what is ?

The curve has a horizontal tangent at which of the following points? Select all that apply.

Given , find .

Quiz 3: Shortcuts to Differentiation

Find the first derivative of w = x2 + ax.

The equation for the tangent line to the curve when x = 3 is y = _____x + _____.

Find the first derivative of .

Given , find .

Find the first derivative of .

Find the first derivative of .

Find the first derivative of .

The equation for the tangent line to the function at x = 1 is y = _____x + _____.

Find the first derivative of .

A. The equation for the tangent line to the curve when x = 4 is y = _____x + _____. B. The tangent line meets the y-axis at y = _____ and the x-axis at x = _____.

Find the first derivative of

Find the derivative of .

If , find

Find the first derivative of w(x) = bx2 + xu.

Find the first derivative of .

The total cost, in dollars, to produce q units is given by . Find

Find the derivative of

If for , what is ?

The curve has a horizontal tangent at which of the following points? Select all that apply.

Given , find .

Find the first derivative of w = x²+ ax.

The equation for the tangent line to the curve when x = 3 is y = _x + _.

The equation for the tangent line to the function at x = 1 is y = _x + _.

A. The equation for the tangent line to the curve when x = 4 is y = ___x + _. B. The tangent line meets the y-axis at y = _ and the x-axis at x = ___.

Find the first derivative of w(x) = bx²+ x^u^.