Find the derivative of e^x-1e^(-1x)

\frac{d}{dx}\left(e^x-e^{-x}\right)

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Answer

$e^{-x}+e^x$

Step by step solution

Problem

$\frac{d}{dx}\left(e^x-e^{-x}\right)$
1

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(-e^{-x}\right)+\frac{d}{dx}\left(e^x\right)$
2

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$\frac{d}{dx}\left(e^x\right)-\frac{d}{dx}\left(e^{-x}\right)$
3

Applying the derivative of the exponential function

$e^x-\frac{d}{dx}\left(e^{-x}\right)$
4

Applying the derivative of the exponential function

$e^x-1\cdot 1\frac{d}{dx}\left(-x\right)e^{-x}$
5

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$e^x-1\cdot 1\left(-1\right)e^{-x}\cdot\frac{d}{dx}\left(x\right)$
6

The derivative of the linear function is equal to $1$

$e^x-1\cdot 1\cdot 1\left(-1\right)e^{-x}$
7

Multiply $-1$ times $-1$

$1e^{-x}+e^x$
8

Any expression multiplied by $1$ is equal to itself

$e^{-x}+e^x$

Answer

$e^{-x}+e^x$

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Problem Analysis

Main topic:

Differential calculus

Time to solve it:

0.2 seconds

Views:

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