Suppose f is differentiable on R. Let F(x) = f(e^x) and G(x) = e^f(x). Find expressions for (a)...
Question:
Suppose f is differentiable on {eq}\mathbb{R} {/eq}. Let {eq}F\left( x \right)=f\left( {{e}^{x}} \right) {/eq} and {eq}G\left( x \right)={{e}^{f\left( x \right)}} {/eq}. Find expressions for
(a) {eq}F'(x) {/eq}
(b) {eq}G'(x) {/eq}
Differentiability:
The differentiability of the exponential function having some function in the exponent is obtained using the chain rule by first differentiating the exponential function and then the exponent function; that is, {eq}\dfrac{d}{{dx}}\left( {{e^{h\left( x \right)}}} \right) = {e^{h\left( x \right)}}\dfrac{d}{{dx}}\left( {h\left( x \right)} \right){/eq}.
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(a)
Given:
- The functions are {eq}F\left( x \right) = f\left( {{e^x}} \right){/eq}, {eq}G\left( x \right) = {e^{f\left( x \right)}}{/eq}, and...
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How to Compute Derivatives
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Chapter 20 / Lesson 1
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Understand what derivative calculus is and how to find the derivative of a function. Learn the derivative rules, and practice taking derivatives by following examples.
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