Question

Finding a derivative: use the rule of differentiation to find the derivative of the function

Answer 1

Given the function:

$y=7x^4+2\sin x$

Apply the rule of differentiation:

$\frac{dy}{dx}=\frac{d(7x^4)}{dx}+\frac{d(2\sin x)}{dx}$

Solve:

$\begin{gathered} \frac{d(7x^{4})}{dx}=7\cdot4x^{4-1}=28x^3 \\ \frac{d(2\sin(x))}{dx}=2\cos x \end{gathered}$

Substitute the derivatives:

$\frac{dy}{dx}=28x^3+2\cos x$

Answer:

$\frac{dy}{dx}=28x^{3}+2\cos(x)$