Chaya Galloway

2021-04-11

Find the derivatives of the following functions.
$f\left(x\right)={x}^{2}{\mathrm{cos}h}^{2}3x$

BleabyinfibiaG

Step 1
The given function is:
$f\left(x\right)={x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)$
We know that,
$d\frac{\mathrm{cos}hx}{dx}=\mathrm{sin}hx$
$d\frac{\mathrm{sin}hx}{dx}=\mathrm{cos}hx$
Step 2
Differentiating the above function with respect to x we get,
$d\frac{f\left(x\right)}{dx}=d\frac{{x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)}{dx}$
$d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+{x}^{2}\left[2\left(3\right)\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)\right]$
$d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+6{x}^{2}\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)$
$d\frac{f\left(x\right)}{dx}=2x\mathrm{cos}h\left(3x\right)\left[\mathrm{cos}h\left(3x\right)+3x\mathrm{sin}h\left(3x\right)\right]$