What is the derivative of y=e^{e^{4x^4}} ?

The derivative of y=e^{e^{4x^4}} is 16e^{e^{4x^4}+4x^4}x^3

What is the first derivative of y=e^{e^{4x^4}} ?

The first derivative of y=e^{e^{4x^4}} is 16e^{e^{4x^4}+4x^4}x^3

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derivative of

y = e^{e^{4 x^{4}}}

16 e^{e^{4 x^{4}} + 4 x^{4}} x^{3}

Solution steps

\frac{d}{d x} (e^{e^{4 x^{4}}})

Apply the chain rule:

e^{e^{4 x^{4}}} \frac{d}{d x} (e^{4 x^{4}})

= e^{e^{4 x^{4}}} \frac{d}{d x} (e^{4 x^{4}})

\frac{d}{d x} (e^{4 x^{4}}) = e^{4 x^{4}} \cdot 16 x^{3}

= e^{e^{4 x^{4}}} e^{4 x^{4}} \cdot 16 x^{3}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{e^{4 x^{4}}} e^{4 x^{4}} = e^{e^{4 x^{4}} + 4 x^{4}}

= 16 e^{e^{4 x^{4}} + 4 x^{4}} x^{3}

x \to \frac{1}{3} lim (\frac{x + 4}{x + 5})

\frac{d}{d x} (ln (\frac{1}{csc ( x )}))

x \to \infty lim (\frac{e}{x})

x \to 1 - lim (4 x + 1)

f (x) = 5 x^{e} - x^{\frac{5}{3}} + \frac{2}{x ^{3}}

What is the derivative of y=e^{e^{4x^4}} ?
The derivative of y=e^{e^{4x^4}} is 16e^{e^{4x^4}+4x^4}x^3
What is the first derivative of y=e^{e^{4x^4}} ?
The first derivative of y=e^{e^{4x^4}} is 16e^{e^{4x^4}+4x^4}x^3