What is (\partial)/(\partial x)(e^{4e^x}) ?

The answer to (\partial)/(\partial x)(e^{4e^x}) is 4e^{4e^x+x}

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(\partial)/(\partial x)(e^{4e^x})

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

4 e^{4 e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{4 e^{x}} \cdot 4 e^{x}

Apply exponent rule:

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

e^{4 e^{x}} e^{x} = e^{4 e^{x} + x}

= 4 e^{4 e^{x} + x}

x + \frac{2}{x}

\frac{d}{d x} (3^{s i n (x)} + \frac{e ^{- x}}{2})

5 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (49 - x^{2} - y^{2})

What is (\partial)/(\partial x)(e^{4e^x}) ?
The answer to (\partial)/(\partial x)(e^{4e^x}) is 4e^{4e^x+x}