Question

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

Answer 1

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

Step-by-step 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 $v(x)=2x +0=2x$

$[\because \dfrac{d(ax)}{dx}=a\ , \dfrac{d(a)}{dx}=0 \ \&\ \ \dfrac{d(x^n)}{dx}=nx^{n-1}]$

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 $f'(x)=12x^2 - 6x+36$ .