2012年4月21日 · For a mechanical way to translate the more familiar trigonometric identities to hyperbolic function identities, use $$\cosh x=\cos(ix),\qquad \sinh x=-i\sin(ix).$$ But perhaps an identity for $\cos(4w)$ does not qualify as familiar.

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2015年8月8日 · I need to show that $\cosh^4(x)-\sinh^4(x) = \cosh(2x)$ First I found myself going in circles.. $$\cosh (2 x)=\frac{1}{2} \left(e^{-2 x}+e^{2 x}\right)= \sinh(2x)$$

What is the derivative of cosh (4x) ? What is the first derivative of cosh (4x) ?

EDIT: $\cosh(4x) = \dfrac{1}{2} e^{4x} + \dfrac{1}{2} e^{-4x}$. When $r$ is not a root of the characteristic polynomial, $a y'' + b y' + c y = e^{r x}$ has a solution $\dfrac{e^{rx}}{a r^2 + b r + c}$

What is the derivative of ln (cosh (4x)) ? What is the first derivative of ln (cosh (4x)) ?

There are 2 steps to solve this one. a. We have, the given function. Not the question you’re looking for? Post any question and get expert help quickly. Answer to a. Find the derivative. f (x) = cosh (4x) f ' (x) =

本文介绍了coshx的倍角公式及其推导过程。 倍角公式的应用可以帮助我们更方便地求解双曲函数的值，解决一些与三角函数相关的数学问题。 通过掌握倍角公式的推导过程和应用，我们能够更加灵活地运用双曲函数在数学领域中。 然后，我们可以继续利用倍角公式，将cosh2x展开为coshx的表达式。 最后，我们可以利用已知的coshx和sinhx的值，计算出cosh4x的准确结果。 假设我们需要证明等式cosh^4x-sinh^4x=1。 我们可以利用倍角公式进行证明。 1. 前言. 在学习高等数学 …

\int \cosh^4x\mathrm{d}x=\int \cosh^3x\mathrm{d}(\sinh x)=\bbox[#CFF,5px]{\int p^3\mathrm{d}q} 后面就可以用双元递推式了，公式及其证明参考：

Learn how to solve differential calculus problems step by step online. Find the derivative of cosh(4x). Taking the derivative of hyperbolic cosine. The derivative of the linear function times a constant, is equal to the constant.