What is the derivative of y=e^{5e^x} ?

The derivative of y=e^{5e^x} is 5e^{5e^x+x}

What is the first derivative of y=e^{5e^x} ?

The first derivative of y=e^{5e^x} is 5e^{5e^x+x}

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derivative of

y = e^{5 e^{x}}

5 e^{5 e^{x} + x}

Solution steps

\frac{d}{d x} (e^{5 e^{x}})

Apply the chain rule:

e^{5 e^{x}} \frac{d}{d x} (5 e^{x})

= e^{5 e^{x}} \frac{d}{d x} (5 e^{x})

\frac{d}{d x} (5 e^{x}) = 5 e^{x}

= e^{5 e^{x}} \cdot 5 e^{x}

Apply exponent rule:

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

e^{5 e^{x}} e^{x} = e^{5 e^{x} + x}

= 5 e^{5 e^{x} + x}

What is the derivative of y=e^{5e^x} ?
The derivative of y=e^{5e^x} is 5e^{5e^x+x}
What is the first derivative of y=e^{5e^x} ?
The first derivative of y=e^{5e^x} is 5e^{5e^x+x}