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

The derivative of e^{e^{2x^2}} is 4e^{e^{2x^2}+2x^2}x

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

The first derivative of e^{e^{2x^2}} is 4e^{e^{2x^2}+2x^2}x

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{2 x^{2}}) = e^{2 x^{2}} \cdot 4 x

= e^{e^{2 x^{2}}} e^{2 x^{2}} \cdot 4 x

Apply exponent rule:

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

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

= 4 e^{e^{2 x^{2}} + 2 x^{2}} x

f (w) = \frac{w}{w + \frac{d}{w}}

\int \frac{x}{3 x + 2} d x

x \to - 4 lim (2 x + 3)

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 2 y^{3})

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

What is the derivative of e^{e^{2x^2}} ?
The derivative of e^{e^{2x^2}} is 4e^{e^{2x^2}+2x^2}x
What is the first derivative of e^{e^{2x^2}} ?
The first derivative of e^{e^{2x^2}} is 4e^{e^{2x^2}+2x^2}x