How to solve these given? y = e x 2 − 16

Solve for the derivatives of the exponential and natural logarithmic functions:The given function is y = e x 2 − 16 Obtain the derivative as follows. d y d x = d d x ( e x 2 − 16 ) = e x 2 − 16 d d x ( x 2 − 16 ) = e x 2 − 16 1 2 x 2 − 16 d d x ( x 2 − 16 ) = e x 2 − 16 1 2 x 2 − 16 ( 2 x ) = e x 2 − 16 x x 2 − 16 Thus, the derivative is d y d x = e x 2 − 16 x x 2 − 16

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High School
Calculus and Analysis
Calculus 1
Logarithmic Functions

tramolatzqvg

Answered question

2022-11-10

How to solve these given?

y = e^{\sqrt{x^{2} - 16}}

Answer & Explanation

Pignatpmv

Beginner2022-11-11Added 22 answers

Solve for the derivatives of the exponential and natural logarithmic functions:
The given function is

y = e^{\sqrt{x^{2} - 16}}

Obtain the derivative as follows.

\frac{d y}{d x} = \frac{d}{d x} (e^{\sqrt{x^{2} - 16}}) = e^{\sqrt{x^{2} - 16}} \frac{d}{d x} (\sqrt{x^{2} - 16}) = e^{\sqrt{x^{2} - 16}} \frac{1}{2 \sqrt{x^{2} - 16}} \frac{d}{d x} (x^{2} - 16) = e^{\sqrt{x^{2} - 16}} \frac{1}{2 \sqrt{x^{2} - 16}} (2 x) = e^{\sqrt{x^{2} - 16}} \frac{x}{\sqrt{x^{2} - 16}}

Thus, the derivative is

\frac{d y}{d x} = e^{\sqrt{x^{2} - 16}} \frac{x}{\sqrt{x^{2} - 16}}

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