Question

Differentiate:
y=5^(3x)

Answer 1

Do you take the natural log of each side?

Answer 2

You know that \[\frac{d}{dx}a^x=a^x\ln{a}\]right?
And you can rewrite \(5^{3x}\) as \((5^3)^x\).

Answer 3

I got y'=5^(3x)*(ln5)

Answer 4

There's something missing there.

Answer 5

Yeah its suppose to be 3ln5, but does that 3 come from when you take the derivative of 3x?

Answer 6

Yep, that's what you get when you apply the chain rule.

Answer 7

thank you! How do you simplify

dy/dx= y(2+2lnx)

Answer 8

What do you mean by simplify?

Answer 9

The next step.. The problem is y=x^(2x)

Answer 10

You plug in y=x^(2x) into the equation for dy/dx.

Answer 11

Seriously!? I've been here over thinking this. Thanks so much