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

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

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

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

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derivative of

y = e^{e^{x}}

e^{e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{e^{x}} e^{x}

Apply exponent rule:

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

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

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

x x + 1

(1, - 6), (- 3, 4)

x^{3} + y^{3} = 6 x y

y = x, (1, 1)

(2, \frac{3 π}{4})

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