What is the derivative of ln[5x - e^x^2] ?

Question

Please help me understand which rules to follow. Thanks!!

Answer 1

using chain rule this is equal to
1/[5x-e^x^2]*d/dx of [5x-e^x^2]
=[1/(5x-e^x^2)]*[5-e^x^2*d/dx of x^2]
=[1/(5x-e^x^2)]*[5-2xe^x^2]

Answer 2

ln(5x - e^x^2) = (5 - 2x(e^x^2))/(5x - (e^x^2))

www.quickmath.com can Differentiate this for you.

Answer 3

derivative of f(g(x)) is f'(g(x)). g'(x)

eg: derivative of e^(x^2) = e^(x^2) . 2x
derivative of sin(cos(x)) = cos(cos(x)). -sin(x)

here,

derivative = 1/(5x-e^(x^2)) (5-2x.e^(x^2))