When I use the powers rule to find the derivative of f(x)=(x^3+5x)^7, I get f'(x)=7(x^3+5x)^6. When I use the chain rule to find the derivative of the same equation, I get 7(5x^3+5x)^6(3x^2+5). Any idea what my mistake is?

Question

psymon · Answer

You dont really get an option of which you do, power or chain rule, you kind of just have to do the chain rule. So if you took the derivative you would need the chain rule, giving you
$$7(x^{3} + 5x)^{6} (3x^{2}+5) $$

anonymous · Answer

your f(x) is really a chain function therefore you have to use chain rule

anonymous · Answer

So I always have to use the chain rule?

anonymous · Answer

technially, yes.

chain rule on x^3 is 3x^2*(x') which is 3x^2 * 1 = 3x^2

anonymous · Answer

I see. Thanks for the help!