What is the derivative of e^{4^x} ?

The derivative of e^{4^x} is e^{4^x}ln(2)*2^{2x+1}

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

The first derivative of e^{4^x} is e^{4^x}ln(2)*2^{2x+1}

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\frac{d}{d x} (e^{4^{x}})

e^{4^{x}} ln (2) \cdot 2^{2 x + 1}

Solution steps

\frac{d}{d x} (e^{4^{x}})

Apply the chain rule:

e^{4^{x}} \frac{d}{d x} (4^{x})

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

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

= e^{4^{x}} ln (2) \cdot 2^{2 x + 1}

What is the derivative of e^{4^x} ?
The derivative of e^{4^x} is e^{4^x}ln(2)*2^{2x+1}
What is the first derivative of e^{4^x} ?
The first derivative of e^{4^x} is e^{4^x}ln(2)*2^{2x+1}