Find the differential of the function at the indicated number.
Select the correct answer.
$$f ( x ) = \sqrt { x ^ { 2 } + 7 } ; \quad x = 3$$
A) $\frac { 3 } { 8 } d x$
B) $\frac { 3 } { 4 } d x$
C) $\frac { 3 } { 2 } d x$
D) $\frac { 1 } { 8 } d x$

Question

Quizplus · Accepted Answer

First, we differentiate the function:
$$f'(x)=\frac{x}{\sqrt{x^2+7}}$$
Then, plugging in $x=3$, we get:
$$f'(3)=\frac{3}{\sqrt{3^2+7}}=\frac{3}{4}$$
So the correct answer is B, $\frac{3}{4}dx$.

Find the Differential of the Function at the Indicated Number f(x)=x2+7;x=3f ( x ) = \sqrt { x ^ { 2 } + 7 } ; \quad x = 3f(x)=x2+7​;x=3

Find the Differential of the Function at the Indicated Number $f ( x ) = \sqrt { x ^ { 2 } + 7 } ; \quad x = 3$