# Derivatives of hyperbolic trigonometric functions Calculator

## Get detailed solutions to your math problems with our Derivatives of hyperbolic trigonometric functions step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Solved example of derivatives of hyperbolic trigonometric functions

$\frac{d}{dx}\left(csch^2\left(4x^3+1\right)\right)$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2csch\left(4x^3+1\right)^{\left(2-1\right)}\frac{d}{dx}\left(csch\left(4x^3+1\right)\right)$

Subtract the values $2$ and $-1$

$2csch\left(4x^3+1\right)\frac{d}{dx}\left(csch\left(4x^3+1\right)\right)$
2

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2csch\left(4x^3+1\right)\frac{d}{dx}\left(csch\left(4x^3+1\right)\right)$

Taking the derivative of hyperbolic cosecant

$2\left(-1\right)csch\left(4x^3+1\right)csch\left(4x^3+1\right)coth\left(4x^3+1\right)\frac{d}{dx}\left(4x^3+1\right)$

Multiply $2$ times $-1$

$-2csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(4x^3+1\right)$
3

Taking the derivative of hyperbolic cosecant

$-2csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(4x^3+1\right)$

4

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

$-2csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\left(\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(1\right)\right)$

The derivative of the constant function ($1$) is equal to zero

$-2csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\left(\frac{d}{dx}\left(4x^3\right)+0\right)$

$x+0=x$, where $x$ is any expression

$-2csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(4x^3\right)$
5

The derivative of the constant function ($1$) is equal to zero

$-2csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(4x^3\right)$

The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function

$-2\cdot 4csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(x^3\right)$

Multiply $-2$ times $4$

$-8csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(x^3\right)$
6

The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function

$-8csch\left(4x^3+1\right)^2coth\left(4x^3+1\right)\frac{d}{dx}\left(x^3\right)$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$-8\cdot 3csch\left(4x^3+1\right)^2x^{\left(3-1\right)}coth\left(4x^3+1\right)$

Subtract the values $3$ and $-1$

$-24csch\left(4x^3+1\right)^2x^{2}coth\left(4x^3+1\right)$
7

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$-24csch\left(4x^3+1\right)^2x^{2}coth\left(4x^3+1\right)$

$-24csch\left(4x^3+1\right)^2x^{2}coth\left(4x^3+1\right)$