What is the derivative of e^{e^{2x}} ?

The derivative of e^{e^{2x}} is 2e^{e^{2x}+2x}

What is the first derivative of e^{e^{2x}} ?

The first derivative of e^{e^{2x}} is 2e^{e^{2x}+2x}

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\frac{d}{d x} (e^{e^{2 x}})

2 e^{e^{2 x} + 2 x}

Solution steps

\frac{d}{d x} (e^{e^{2 x}})

Apply the chain rule:

e^{e^{2 x}} \frac{d}{d x} (e^{2 x})

= e^{e^{2 x}} \frac{d}{d x} (e^{2 x})

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= e^{e^{2 x}} e^{2 x} \cdot 2

Apply exponent rule:

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

e^{e^{2 x}} e^{2 x} = e^{e^{2 x} + 2 x}

= 2 e^{e^{2 x} + 2 x}

\int \frac{2 x + 1}{x ^{2} + 2 x + 65} d x

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

\int sin^{3} (b) cos^{3} (b)

x \to - 2 lim (x^{4} + 5^{x} - 2)

\frac{\partial}{\partial y} (x ln (x + 2 y + 3 z))

What is the derivative of e^{e^{2x}} ?
The derivative of e^{e^{2x}} is 2e^{e^{2x}+2x}
What is the first derivative of e^{e^{2x}} ?
The first derivative of e^{e^{2x}} is 2e^{e^{2x}+2x}