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Chapter 2: Q 19. (page 237)

Fill in the blank:
$\frac{d}{d x} (e^{x}) = - - -$

Short Answer

Expert verified

$\frac{d}{d x} (e^{x}) = e^{x}$

Step by step solution

Given Information

The given expression is $\frac{d}{d x} (e^{x})$

Simplification

We know that

\frac{d}{d x} (e^{f (x)}) = e^{f (x)} . f^{'} (x)

$\Rightarrow \frac{d}{d x} (e^{x}) = e^{x} . \frac{d}{d x} (x)$

$= e^{x}$

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Most popular questions from this chapter

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

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Suppose $u (x) = \sqrt{3 x^{2} + 1}$ and $f (u) = \frac{u^{2} + 3 u^{5}}{1 - u}$ . Use the chain rule to find role="math" localid="1648356625815" $\frac{d}{d x} (f (u (x)))$ without first finding the formula for $f (u (x))$ .

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26. $f (x) = \frac{1}{x^{2}}, x = 2$

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Fill in the blank:ddxex=---

Short Answer

Step by step solution

Given Information

Simplification

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Fill in the blank:
$\frac{d}{d x} (e^{x}) = - - -$