# 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

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

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

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

Taking the derivative of hyperbolic cosecant

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

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

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

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

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

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

$-8\mathrm{csch}\left(4x^3+1\right)^2\mathrm{coth}\left(4x^3+1\right)\frac{d}{dx}\left(x^3\right)$
7

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

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

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