Find the derivatives of the following functions. f(t)=coshtsinht

glasskerfu

Answered question

2021-03-03

Find the derivatives of the following functions.
$f\left(t\right)=\mathrm{cos}ht\mathrm{sin}ht$

Answer & Explanation

2abehn

Skilled2021-03-05Added 88 answers

Given, $f\left(t\right)=\mathrm{cos}ht\mathrm{sin}ht$ Differentiating with respect to t, we get ${f}^{\prime}\left(t\right)=\frac{d\left(\mathrm{cos}ht\right)}{dt}\cdot \mathrm{sin}ht+\frac{d\left(\mathrm{sin}ht\right)}{dt}\cdot \mathrm{cos}ht$ $=\mathrm{sin}ht\cdot \mathrm{sin}ht+\mathrm{cos}ht\cdot \mathrm{cos}ht$ $={\mathrm{sin}h}^{2}t+{\mathrm{cos}h}^{2}t$ $=\mathrm{cos}h\left(2t\right)$