Question

How do you differentiate `g(x) = (5x^6 - 4) sin(6x)` using the product rule?

Answer 1

The product rule is `d/dx(uv)=u(dv)/dx+(du)/dxv`

Let `u(x)=5x^6-4 and v(x)=sin6x`

Then, `(du)/dx=(5x^5)6=30x^5`
And, `(dv)/dx=(cos6x)6 =6cos6x`

So the product rue gives:

`(dg)/dx=(5x^6-4)(6cos6x) + (30x^5)(sin6x)`
`:.(dg)/dx=30x^6cos6x-24cos6x+30x^5sin6x`