Question

Find dy/dx if y=ln(x^2+5x)
My teacher said it was (2x+5)/(x^2+5x)
But I don't know how to get the answer.
Please help me.

Answer 1

well when you differentiate a log function

\[y = \ln(f(x)\]

the result is a fraction, the derivative over the function

\[\frac{dy}{dx} = \frac{f'(x)}{f(x)}\]

so in your question the function is \[f(x) = x^2 + 5x\]

then the derivative is

\[f'(x) = 2x + 5\]