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

The derivative of e^{4e^x} is 4e^{4e^x+x}

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

The first derivative of e^{4e^x} is 4e^{4e^x+x}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Apply exponent rule:

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

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

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

\int \frac{1}{x x ^{4} + 1} d x

\int \frac{2 x}{16 x ^{4} - 9} d x

2 x e^{x} cos (x)

\frac{d}{d x} (ln (\frac{x ^{\frac{1}{2}}}{3}))

\int (x^{2} - 3) d x

What is the derivative of e^{4e^x} ?
The derivative of e^{4e^x} is 4e^{4e^x+x}
What is the first derivative of e^{4e^x} ?
The first derivative of e^{4e^x} is 4e^{4e^x+x}