What is the derivative of e^{8e^x}*8e^x ?

The derivative of e^{8e^x}*8e^x is 8e^{8e^x+x}(8e^x+1)

What is the first derivative of e^{8e^x}*8e^x ?

The first derivative of e^{8e^x}*8e^x is 8e^{8e^x+x}(8e^x+1)

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derivative of

e^{8 e^{x}} \cdot 8 e^{x}

8 e^{8 e^{x} + x} (8 e^{x} + 1)

Solution steps

\frac{d}{d x} (e^{8 e^{x}} \cdot 8 e^{x})

Simplify

e^{8 e^{x}} \cdot 8 e^{x} : 8 e^{8 e^{x} + x}

= \frac{d}{d x} (8 e^{8 e^{x} + x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (e^{8 e^{x} + x})

Apply the chain rule:

e^{8 e^{x} + x} \frac{d}{d x} (8 e^{x} + x)

= e^{8 e^{x} + x} \frac{d}{d x} (8 e^{x} + x)

\frac{d}{d x} (8 e^{x} + x) = 8 e^{x} + 1

= 8 e^{8 e^{x} + x} (8 e^{x} + 1)

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\frac{\partial}{\partial x} (\frac{100}{4 x ^{2} + y ^{2}})

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What is the derivative of e^{8e^x}*8e^x ?
The derivative of e^{8e^x}*8e^x is 8e^{8e^x+x}(8e^x+1)
What is the first derivative of e^{8e^x}*8e^x ?
The first derivative of e^{8e^x}*8e^x is 8e^{8e^x+x}(8e^x+1)