Question

find the derivatives

Answer 1

Let's start with the first one.\[\frac{d}{dx}[e^{x^{3}}+\log_{4}(\pi)]\]
The first term can be derivated normally. We need to multiply by the derivative of its power as well. The second term doesn't depend on x, so it is a constant in this. Therefore, it's derivative is 0.\[\frac{d}{dx}=e^{x^{3}}(3x^{2}) +0=3x^{2}e^{x^{3}}\]

Answer 2

what rule did you use for it?

Answer 3

Umm, I think it's called the chain rule.

Answer 4

oh ok thanks now i see it

Answer 5

The second one looks ugly. You could make it look a little neater:\[\frac{d}{dx}[x^{\frac{\ln(x)}{6}}]\]

Answer 6

would the power go to the front? or no

Answer 7

No, because this isn't the case of x^n, rather the power is also a function of x. This one is a little tricky actually.

If i'm not mistaken you can rewrite the integral in a form that is doable.

Answer 8

how would i rewrite it then?

Answer 9

\[\frac{d}{dx}[x^{\frac{\ln(x)}{6}}]=\frac{d}{dx}[e^{\ln(\frac{xln(x)}{6})}]\]
I'm not sure if this is right, i'm just writing it out to see what it looks like. I'm thinking you can exponentiate it all.

Answer 10

the e and ln wont cancel out?

Answer 11

That's the point! :D They do cancel out, but that is why I wrote it. We may be able to derivate this expression. Since they cancel out, it means the statement I wrote is equivalent to the one we originally had.

Answer 12

it's just a different form of the same thing

Answer 13

Again, not sure if it's the correct way to try and proceed. I'm testing it now.

Answer 14

oh ok then i guess we can try it

Answer 15

so we would be left with?