Find the derivative of x-11/x

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

Go!
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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

Answer

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

Step by step solution

Problem

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

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

$\frac{d}{dx}\left(-\frac{1}{x}\right)+\frac{d}{dx}\left(x\right)$
2

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

$\frac{d}{dx}\left(-\frac{1}{x}\right)+1$
3

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

$1-\frac{d}{dx}\left(\frac{1}{x}\right)$
4

Taking the derivative of the hyperbolic sine

$1-\frac{d}{dx}\left(x\right)cosh\left(x\right)$
5

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

$1-1\cdot 1cosh\left(x\right)$
6

Multiply $1$ times $-1$

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

Answer

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

Problem Analysis

Main topic:

Differential calculus

Time to solve it:

0.18 seconds

Views:

116

All topics:

Differential calculus