How do you do the derivative of a^x, for example, (3/4)^x

Question

Thank you for helping!

Answer 1

recall that if y = e^u where u is a function of x,

y' = e^u du/dx

Now, a^x = (e^(ln a))^x = e^(x*ln a)

so, y' = e^(x*ln a) * ln a = ln a * a^x

makes sense, since if a>e, ln a > 1, and the curve rises more steeply

Answer 2

Use the exponent rule. Bring the exponent down in front and then reduce your exponent by 1.

a^x = x(a^(x-1))

(3/4)^5 = 5(3/4)^4