Question

What is the second derivative of `f(x)= 2x^3- sqrt(4x-5)`?

Answer 1

`12x + 4/(4x - 5 )^(3/2)`

Explanation:

to obtain the second derivative means differentiating the function to obtain f'(x) and then differentiating f'(x) to obtain f''(x).

rewriting f(x) as `f(x) = 2x^3 - (4x - 5 )^(1/2)`

applying the chain rule :

`f'(x) = 6x^2 - 1/2 (4x - 5 )^(-1/2).d/dx(4x - 5 )`

`f'(x) = 6x^2 - 1/2 (4x - 5 ).4 = 6x^2 - 2(4x - 5 )^(-1/2)`

`f''(x) = 12x + (4x - 5 )^(-3/2).d/dx(4x - 5 )`

`rArr f''(x) = 12x + (4x - 5 )^(-3/2).4 = 12x + 4/(4x - 5 )^(3/2)`