Question

Find the derivative of the given function: $\sin (3x+5)$.

Answer 1

Compute the required derivative:

Given that, $y=\sin (3x+5)$

Now, if we apply derivative on the given function with respect to $x$then the equation becomes,

$$\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}\left[\sin \right(3x+5\left)\right] \\ \frac{dy}{dx}=\left[\cos \right(3x+5\left)\right]\times \frac{d}{dx}(3x+5) \\ \frac{dy}{dx}=\left[\cos \right(3x+5\left)\right]\times \left[\frac{d}{dx}\right(3x)+\frac{d}{dx}(5\left)\right] \\ \frac{dy}{dx}=3\left[\cos \right(3x+5\left)\right] \end{gathered}$$ $\left[\therefore \frac{d}{dx}\left(\sin x\right)=\cos x,\frac{d}{dx}\left(x\right)=1\right]$

Hence, the derivative of the given function: $\sin (3x+5)$ is $\frac{dy}{dx}=3\left[\cos \right(3x+5\left)\right]$.