Differentiate with respect to x

Question

 

f(x) = x^3 - 2x^2 - 5x - 12 / 4x^2 - 9?

Answer 1

f(x) = x^3 - 2x^2 - 5x - 12 / 4x^2 - 9

Recall the quotient rule d/dx(u/v)= [ u'·v -u·v' ] / v²(x)

Here u = x³-2x²-5x-12;v = 4x²-9

u'(x) =3x²-4x-5;v'(x) =8x

f'(x)=(3x²-4x-5)(4x²-9)-(x³-2x²-5x-12)(8x)/(4x²-9)^2

           =12x⁴-27x²-16x³-36x-20x²+45-8x⁴+16x³-40x²-96x/16x⁴-72x²+81

        =4x⁴-87x²-132x+45/16x⁴-72x²+81

The derivative of the given function is 4x⁴-87x²-132x+45/16x⁴-72x²+81

Hope that helps u