How do you find the derivative of this? please explain:)

drawn inside!

Question

How do you find the derivative of this? please explain:)

drawn inside!

anonymous · Answer

|dw:1394419917205:dw|

anonymous · Answer

also, what is the mathematical term for where the 7 is? it's some root? i forget the technical term :/

anonymous · Answer

These are power functions.

anonymous · Answer

The position is called the radix, I believe.

anonymous · Answer

You could call it the "seventh root". I can't make out the second term's power, but for the first, you can write
$$\sqrt[7]{x^2}=x^{2/7}$$
which as @wio mentioned can be differentiated with the power rule.

anonymous · Answer

oh okay... oh here's the second term, sorry it wasn't clear! x^e

here's the entire function:) $$\sqrt[7]{x^2} - x^e$$

anonymous · Answer

i know that d/dx (e^x) = e^x

is that the same for when it's x^e? would d/dx (x^e) = x^e ?

anonymous · Answer

No, the derivative is just another use of the power rule.

For a *constant* $n$, you have
$$\frac{d}{dx}x^n=nx^{n-1}$$
$e$ is a constant.

anonymous · Answer

okay, so would i get this?|dw:1394420390206:dw| ?