I assume you know the chain rule, and that
d/dx e^u = e^u du/dx
Now, for some other base, such as 5, recall that
5 = e^ln5
So, 5^x = e^(ln5 x)
d/dx 5^x = ln5 e^(ln5 x) = ln5 5^x
So we arrive at the fact that
d/dx a^u = ln(a) a^u du/dx
and your result follows.
Find the derivative of 5^(x^3+x)
I know the answer, it's:
5^(x^3+x)*ln(5)*(3x^2+ 1)
I just need some help on how to derive that. What rule is at work here? where did the ln come from?
1 answer