What is the derivative of e^{a(e^x-1}) ?

The derivative of e^{a(e^x-1}) is ae^{a(e^x-1)+x}

What is the first derivative of e^{a(e^x-1}) ?

The first derivative of e^{a(e^x-1}) is ae^{a(e^x-1)+x}

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Popular >

\frac{d}{d x} (e^{a (e^{x} - 1)})

a e^{a (e^{x} - 1) + x}

Solution steps

\frac{d}{d x} (e^{a (e^{x} - 1)})

Apply the chain rule:

e^{a (e^{x} - 1)} \frac{d}{d x} (a (e^{x} - 1))

= e^{a (e^{x} - 1)} \frac{d}{d x} (a (e^{x} - 1))

\frac{d}{d x} (a (e^{x} - 1)) = a e^{x}

= e^{a (e^{x} - 1)} a e^{x}

Apply exponent rule:

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

e^{a (e^{x} - 1)} e^{x} = e^{a (e^{x} - 1) + x}

= a e^{a (e^{x} - 1) + x}

\frac{1}{s}

y = 27 - x^{2}, y = 6 x, y = \frac{2}{5} x

sin (3 x)

\frac{d y}{d x} = 3 x (x - 1)

x \to 0 lim (3 x^{3} + 6 x^{2} + 7 x)

What is the derivative of e^{a(e^x-1}) ?
The derivative of e^{a(e^x-1}) is ae^{a(e^x-1)+x}
What is the first derivative of e^{a(e^x-1}) ?
The first derivative of e^{a(e^x-1}) is ae^{a(e^x-1)+x}