Question

In Exercise find the derivative of the functions.
f(x) = (4x - 3)(x2 + 9)

Answer 1

Answer:
`f'(x)=12x^2 - 6x+36`

Explanation:

According to the product rule of derivatives.

`f'(x)=u'(x)v(x)+u(x)v'(x)`

The given function :
`f(x) = (4x - 3)(x^2 + 9)`

here ,
`u(x) = 4x - 3` and
`v(x)=x^2 + 9`

Differentiate both sides with respect to x, we get

`u'(x) = 4+0=4` and
`v(x)=2x +0=2x`

`[\because (d(ax))/(dx)=a\ , (d(a))/(dx)=0 \ \&\ \ (d(x^n))/(dx)=nx^(n-1)]`

Then, Tge derivative of withe respect to x will be :

`f'(x)=u'(x)v(x)+u(x)v'(x)`

`=4(x^2 + 9)+( 4x - 3)(2x)`

`=4x^2 +36+8x^2 - 6x`

`=12x^2 - 6x+36`

Hence, the derivative of the function is
`f'(x)=12x^2 - 6x+36` .