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

The derivative of y=e^{8e^x} is 8e^{8e^x+x}

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

The first derivative of y=e^{8e^x} is 8e^{8e^x+x}

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derivative of

y = e^{8 e^{x}}

8 e^{8 e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Apply exponent rule:

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

e^{8 e^{x}} e^{x} = e^{8 e^{x} + x}

= 8 e^{8 e^{x} + x}

\frac{d}{d x} (\frac{1}{8} x^{4} + \frac{1}{4} x^{- 2})

y^{^{''}} + 25 y = cos (3 t)

\int_{0}^{\infty} E (t) d t

\frac{d}{d x} (2 x^{3})

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

What is the derivative of y=e^{8e^x} ?
The derivative of y=e^{8e^x} is 8e^{8e^x+x}
What is the first derivative of y=e^{8e^x} ?
The first derivative of y=e^{8e^x} is 8e^{8e^x+x}