Determine the values of a and b.

Question

The derivative of f(x)=(2x+3)(4x+5)³ is given as f'(x)=2(4x+5)²(ax+b)

Answer 1

Using product rule of differentiation

f'(x)=(2x+5)'(4x+5)^3+(2x+5)((4x+5)^3)'

=2(4x+5)^3+(2x+5)*(3*(4x+5)^2*4)

=(4x+5)^2(2(4x+5)+12*(2x+5))

=(4x+5)^2(8x+10+24x+60)

=(4x+5)^2(32x+70)

=2(4x+5)^2(16x+35)

So, a=16,b=35