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Chapter 2: Q27. (page 222)

Find the derivatives of the functions: $f (x) = e^{(e^{x})}$

Short Answer

Expert verified

The required answer is $e^{(e^{x})} e^{x}$ .

Step by step solution

Step 1. Given information.

The given function is: $e^{(e^{x})}$

Step 2. Find the derivative of the given function.

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

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Most popular questions from this chapter

Find the derivative of the absolute value function and piecewise defined function

$f (x) = \{\begin{cases} 3 x + 1 & i f x \leq 1 \\ x^{3} & i f x > 1 \end{cases}$

For each function $f$ graphed in Exercises 65-68, determine the values of $x$ at which $f$ fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

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.

$f (x) = x^{- \frac{1}{2}} {(x^{2} - 1)}^{3}$

In Exercises 69–80, determine whether or not $f$ is continuous and/or differentiable at the given value of $x$ . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.

$f (x) = \{\begin{cases} x^{2}, i f x \leq 1 \\ 2 x - 1, i f x > 1, \end{cases} x = 1$

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

$f' (x) = (x^{4} - 8) (1 - 3 x^{5}); f (0) = 2$

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Find the derivatives of the functions:f(x)=e(ex)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative of the given function.

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Most popular questions from this chapter

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Find the derivatives of the functions: $f (x) = e^{(e^{x})}$