What is the derivative of e^{6e^x} ?

The derivative of e^{6e^x} is 6e^{6e^x+x}

What is the first derivative of e^{6e^x} ?

The first derivative of e^{6e^x} is 6e^{6e^x+x}

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derivative of

e^{6 e^{x}}

6 e^{6 e^{x} + x}

Solution steps

\frac{d}{d x} (e^{6 e^{x}})

Apply the chain rule:

e^{6 e^{x}} \frac{d}{d x} (6 e^{x})

= e^{6 e^{x}} \frac{d}{d x} (6 e^{x})

\frac{d}{d x} (6 e^{x}) = 6 e^{x}

= e^{6 e^{x}} \cdot 6 e^{x}

Apply exponent rule:

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

e^{6 e^{x}} e^{x} = e^{6 e^{x} + x}

= 6 e^{6 e^{x} + x}

\int_{0}^{1} (2 x - 2 x^{2}) d x

\frac{d}{d x} (x^{4} + x^{3} + x^{2} + 1)

\int \frac{2 x + 3}{x} d x

f (x) = 4 - x^{2}, (- 1, 3)

7 x sin (x)

What is the derivative of e^{6e^x} ?
The derivative of e^{6e^x} is 6e^{6e^x+x}
What is the first derivative of e^{6e^x} ?
The first derivative of e^{6e^x} is 6e^{6e^x+x}