Question

find the derivative of y=e^(4)^(x)^(4)

Answer 1

\[y=e ^{4^{x ^{4}}}\] it can also be written like this as well

Answer 2

chain rule it all the way down

Answer 3

What @satellite73 said; also, these derivative formulas will come in handy here:

\(\dfrac{d}{dx}e^u = e^u\cdot\dfrac{du}{dx}\)

\(\dfrac{d}{dx}a^u = a^u\ln a \cdot \dfrac{du}{dx}\)

Answer 4

\[\frac{d}{dx} (y) = \frac{d}{dx} e^{{4}^{x^4}}\]\[\ y'(x) = e^{4^{x^4}} \cdot \frac{d}{dx} (4^{x^4})\]\[\ y'(x) = e^{4^{x^4}} \cdot 4^{x^4} \cdot \log(4) \cdot \frac{d}{dx} x^4\]

Answer 5

My internet browser is messing up my latex hardcore. Goodness,

Answer 6

\[\ y'(x) = e^{4^{x^4}} \cdot \color{red}{ 4^{x^4}} \cdot \log(4) \cdot \color{red}{4^1}x^3\] combine these. \[\ y'(x) =\color{red}{4^{1+x^4}} \cdot e^{4^{x^4}}\cdot x^3\log(4)\]

Answer 7

thank you! This make so much sense now!

Answer 8

Yay :) I'm glad.