Question

Find the derivative of:
y= 5^x + 15/x^6

I'm assuming I need to take the natural log of each side, but I get stuck after that part.

Answer 1

I would split it into two problems and add the result.

y = 5^x
ln y = x ln 5
y'/y = ln 5
y' = y ln 5
y' = 5^x ln 5
then
y = 15 x^-6
y' = 15(-6) x^-7
y' = -90/x^7
so finally
y' = 5^x ln 5 - 90/x^7