Find the derivative of ((((x^22+x^2x^2+2)^0.5)/(x^2))/((x^22+x^2x^2+2)^0.5))/(x^2x^2)

\frac{d}{dx}\left(\frac{\frac{\frac{\sqrt{2+x^{22}+x^2 x^2}}{x^2}}{\sqrt{2+x^{22}+x^2 x^2}}}{x^2 x^2}\right)

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Answer

$cosh\left(x\right)$

Step by step solution

Problem

$\frac{d}{dx}\left(\frac{\frac{\frac{\sqrt{2+x^{22}+x^2 x^2}}{x^2}}{\sqrt{2+x^{22}+x^2 x^2}}}{x^2 x^2}\right)$
1

When multiplying exponents with same base we can add the exponents

$\frac{d}{dx}\left(\frac{\frac{\frac{\sqrt{x^{4}+x^{22}+2}}{x^2}}{\sqrt{x^{\left(2+2\right)}+x^{22}+2}}}{x^{\left(2+2\right)}}\right)$
2

Add the values $2$ and $2$

$\frac{d}{dx}\left(\frac{\frac{\frac{\sqrt{x^{4}+x^{22}+2}}{x^2}}{\sqrt{x^{4}+x^{22}+2}}}{x^{4}}\right)$
3

Simplifying the fraction

$\frac{d}{dx}\left(\frac{\frac{\sqrt{x^{4}+x^{22}+2}}{x^2}}{x^{4}\sqrt{x^{4}+x^{22}+2}}\right)$
4

Simplifying the fraction

$\frac{d}{dx}\left(\frac{\sqrt{x^{4}+x^{22}+2}}{x^2x^{4}\sqrt{x^{4}+x^{22}+2}}\right)$
5

When multiplying exponents with same base we can add the exponents

$\frac{d}{dx}\left(\frac{\sqrt{x^{4}+x^{22}+2}}{\sqrt{x^{4}+x^{22}+2}x^{6}}\right)$
6

Simplifying the fraction by $\sqrt{x^{4}+x^{22}+2}$

$\frac{d}{dx}\left(\frac{1}{x^{6}}\right)$
7

Taking the derivative of the hyperbolic sine

$\frac{d}{dx}\left(x\right)cosh\left(x\right)$
8

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

$1cosh\left(x\right)$
9

Any expression multiplied by $1$ is equal to itself

$cosh\left(x\right)$

Answer

$cosh\left(x\right)$

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Problem Analysis

Main topic:

Differential calculus

Time to solve it:

0.29 seconds

Views:

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