What is the derivative of 3^{e^x} ?

The derivative of 3^{e^x} is ln(3)*3^{e^x}e^x

What is the first derivative of 3^{e^x} ?

The first derivative of 3^{e^x} is ln(3)*3^{e^x}e^x

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derivative of

3^{e^{x}}

ln (3) \cdot 3^{e^{x}} e^{x}

Solution steps

\frac{d}{d x} (3^{e^{x}})

Apply exponent rule:

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

3^{e^{x}} = e^{e^{x} l n (3)}

= \frac{d}{d x} (e^{e^{x} l n (3)})

Apply the chain rule:

e^{e^{x} l n (3)} \frac{d}{d x} (e^{x} ln (3))

= e^{e^{x} l n (3)} \frac{d}{d x} (e^{x} ln (3))

\frac{d}{d x} (e^{x} ln (3)) = ln (3) e^{x}

= e^{e^{x} l n (3)} ln (3) e^{x}

Simplify

e^{e^{x} l n (3)} ln (3) e^{x} : ln (3) \cdot 3^{e^{x}} e^{x}

= ln (3) \cdot 3^{e^{x}} e^{x}

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What is the derivative of 3^{e^x} ?
The derivative of 3^{e^x} is ln(3)*3^{e^x}e^x
What is the first derivative of 3^{e^x} ?
The first derivative of 3^{e^x} is ln(3)*3^{e^x}e^x