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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Apply exponent rule:

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

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

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

(x^{3} - y^{3}) d x + (x y^{2}) d y = 0

\frac{d y}{d x} = 3 (y + 7) x^{2}

\frac{1 - 3 t}{6 + t}

x \to 0 lim (- sin (x))

\frac{d}{d x} (2 x^{2} - 16 x + 35)

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