Find the derivative of the function. $s ( x ) = 19 \sqrt { x } + \frac { 33 } { \sqrt { x } }$
A) $s ^ { \prime } ( x ) = \frac { 9.5 } { \sqrt { x } } + \frac { 33 } { x \sqrt { x } }$
B) $s ^ { \prime } ( x ) = \frac { 9.5 } { \sqrt { x } } - \frac { 16.5 } { x \sqrt { x } }$
C) $s ^ { \prime } ( x ) = \frac { 19 } { \sqrt { x } } - \frac { 33 } { x \sqrt { x } }$
D) $s ^ { \prime } ( x ) = \frac { 9.5 } { \sqrt { x } } + \frac { 16.5 } { x \sqrt { x } }$
E) $s ^ { \prime } ( x ) = \frac { 8.5 } { \sqrt { x } } + \frac { 17.5 } { x \sqrt { x } }$

Question

Find the derivative of the function.  $s ( x ) = 19 \sqrt { x } + \frac { 33 } { \sqrt { x } }$  
A) $s ^ { \prime } ( x ) = \frac { 9.5 } { \sqrt { x } } + \frac { 33 } { x \sqrt { x } }$
B) $s ^ { \prime } ( x ) = \frac { 9.5 } { \sqrt { x } } - \frac { 16.5 } { x \sqrt { x } }$
C) $s ^ { \prime } ( x ) = \frac { 19 } { \sqrt { x } } - \frac { 33 } { x \sqrt { x } }$
D) $s ^ { \prime } ( x ) = \frac { 9.5 } { \sqrt { x } } + \frac { 16.5 } { x \sqrt { x } }$
E) $s ^ { \prime } ( x ) = \frac { 8.5 } { \sqrt { x } } + \frac { 17.5 } { x \sqrt { x } }$

Quizplus · Accepted Answer

To find the derivative of $s(x) = 19\sqrt{x} + \frac{33}{\sqrt{x}}$, we rewrite the function in terms of $x$ to $s(x) = 19x^{1/2} + 33x^{-1/2}$. Using the power rule for differentiation, $\frac{d}{dx}x^n = nx^{n-1}$, we get $s'(x) = 19\cdot\frac{1}{2}x^{-1/2} - 33\cdot\frac{1}{2}x^{-3/2}$, which simplifies to $s'(x) = \frac{9.5}{\sqrt{x}} - \frac{16.5}{x\sqrt{x}}$.

Find the Derivative of the Function s(x)=19x+33xs ( x ) = 19 \sqrt { x } + \frac { 33 } { \sqrt { x } }s(x)=19x​+x​33​

Find the Derivative of the Function $s ( x ) = 19 \sqrt { x } + \frac { 33 } { \sqrt { x } }$