Question

what is the derivitive of 5^x^2

Answer 1

(5^(x^2))

Answer 2

y = 5^(x^2)
lny = x^2 * ln5
1/y * dy/dx = 2x * ln5 + x^2 * 0
dy/dx = y(2xln5)
dy/dx = 5^(x^2) * 2x * ln5

Answer 3

amirite?

Answer 4

\[y'=5^{2x} \]
\[y'=10x ^{2x-1}\]

Answer 5

you have a choice. you can take the log, differentiate, and then multiply by the original function.
or you can remember that
\[\frac{d}{dx}b^x=b^x\ln(b)\] and use the chain rule

Answer 6

ya i was thinking b^x ln(b)

Answer 7

if you remember that, then this one is easy
just don't forget the chain rule
you get
\[2x\ln(5)\times 5^{x^2}\] in one step