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:

`(dy)/(dx)=(d(7x^4))/(dx)+(d(2\sin x))/(dx)`

Solve:

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

Substitute the derivatives:

`(dy)/(dx)=28x^3+2\cos x`

Answer:

`(dy)/(dx)=28x^(3)+2\cos(x)`