how to find the 1st and 2nd derivatives from

Question

√(5x-2)

f'(x)=

f''(x)=

Answer 1

f(x) = √(5x - 2) = (5x - 2)^1/2

f'(x) = (1/2)(5x-2)^-1/2(5) = (5/2)(5x-2)^-1/2

f"(x) = (5/2)(-1/2)(5x-2)^-3/2(5) = (-25/4)(5x-2)^-3/2

Answer 2

√(5x-2) = (5x - 2)^1/2

Therefore, using the power rule AND the chain rule:

f '(x) = 1/2(5x - 2)^-1/2(5) = 5/2(5x - 2)^-1/2

And, taking the derivative of this, again using the power rule AND the chain rule:

f ''(x) = (-1/2)(5/2)(5x - 2)^-3/2(5) = -25/4(5x - 2)^-3/2