Find the derivative of $g ( x ) = \sqrt { e ^ { x } + e ^ { x ^ { 5 } } }$ .
A) $\sqrt { e ^ { x } + 5 x ^ { 4 } e ^ { x ^ { 5 } } }$
B) $\frac { 1 } { 2 \sqrt { e ^ { x } + e ^ { x ^ { 5 } } } }$
C) $\frac { e ^ { x } + 5 x ^ { 4 } e ^ { x ^ { 5 } } } { 2 \sqrt { e ^ { x } + e ^ { x ^ { 5 } } } }$
D) $\frac { e ^ { x } + x ^ { 5 } e ^ { x ^ { 5 } - 1 } } { 2 \sqrt { e ^ { x } + e ^ { x ^ { 5 } } } }$

Question

Quizplus · Accepted Answer

To find the derivative of $g(x) = \sqrt{e^x + e^{x^5}}$, we use the chain rule. The outer function is the square root, and the inner function is $e^x + e^{x^5}$. The derivative of the outer function, with respect to the inner function, is $\frac{1}{2\sqrt{e^x + e^{x^5}}}$. The derivative of the inner function, with respect to $x$, is $e^x + 5x^4e^{x^5}$. Multiplying these derivatives gives $\frac{e^x + 5x^4e^{x^5}}{2\sqrt{e^x + e^{x^5}}}$.

Find the Derivative Of g(x)=ex+ex5g ( x ) = \sqrt { e ^ { x } + e ^ { x ^ { 5 } } }g(x)=ex+ex5​

Find the Derivative Of $g ( x ) = \sqrt { e ^ { x } + e ^ { x ^ { 5 } } }$