Question

Find the differential of y in the function: y=x^3cosx ?

Answer 1

`dy/dx=3x^2cos(x)-x^3sin(x)`

Explanation:

We want to find the derivative of

`y=x^3cos(x)`

Use the product rule, if `y=f*g`

then `dy/dx=f'*g+f*g'`, thus

• `f=x^3=>f'=3x^2`
• `g=cos(x)=>g'=-sin(x)`

By the product rule

`dy/dx=3x^2cos(x)-x^3sin(x)`