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Popular >

derivative of 2^{e^x}

Solution

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

Solution

ln (2) \cdot 2^{e^{x}} e^{x}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{e^{x}} = e^{e^{x} l n (2)}

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

Apply the chain rule:

e^{e^{x} l n (2)} \frac{d}{d x} (e^{x} ln (2))

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

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

= e^{e^{x} l n (2)} ln (2) e^{x}

Simplify

e^{e^{x} l n (2)} ln (2) e^{x} : ln (2) \cdot 2^{e^{x}} e^{x}

= ln (2) \cdot 2^{e^{x}} e^{x}

Popular Examples

derivative of sqrt(r^2-17x^2)

\frac{d}{d x} (r^{2} - 17 x^{2})

(dy)/(dx)=(-2y)/(x-2)

\frac{d y}{d x} = \frac{- 2 y}{x - 2}

(\partial)/(\partial x)(sqrt(3x^2+y^2))

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

integral of x^2cos(7x)

\int x^{2} cos (7 x) d x

derivative of bcos(t)+t^2sin(t)derivative of

b cos (t) + t^{2} sin (t)

Frequently Asked Questions (FAQ)

What is the derivative of 2^{e^x} ?
The derivative of 2^{e^x} is ln(2)*2^{e^x}e^x
What is the first derivative of 2^{e^x} ?
The first derivative of 2^{e^x} is ln(2)*2^{e^x}e^x