# 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)

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$cosh\left(x\right)$

## 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

$cosh\left(x\right)$

$cosh\left(x\right)$

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

### Main topic:

Differential calculus

0.29 seconds

93