Question

How do you differentiate `f(x)= 5sinx*(1-2x)^2 + cosx*(x+1)` using the product rule?

Answer 1

`d/dx(f(x))=5cosx(1-2x)^2-20sinx(1-2x)-sinx(x+1)+cosx`

Explanation:

According to product rule
`d/dx(u.v)=v(du)/dx+u(dv)/dx`
where u and v are functions of x

`d/dx(5sinx.(1-2x)^2+cosx.(x+1))`
`=(1-2x)^2 d/dx(5sinx)+5sinx d/dx((1-2x)^2)+(x+1) d/dx(cosx)+cosx d/dx(x+1)`
`=(1-2x)^2(5cosx)+5sinx(2(1-2x)(-2))+(x+1)(-sinx)+cosx(1)`
`=5cosx(1-2x)^2-20sinx(1-2x)-sinx(x+1)+cosx`