What is the derivative of e^{xln(a}) ?

The derivative of e^{xln(a}) is a^xln(a)

What is the first derivative of e^{xln(a}) ?

The first derivative of e^{xln(a}) is a^xln(a)

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\frac{d}{d x} (e^{x l n (a)})

a^{x} ln (a)

Solution steps

\frac{d}{d x} (e^{x l n (a)})

Simplify

e^{x l n (a)} : a^{x}

= \frac{d}{d x} (a^{x})

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= a^{x} ln (a)

What is the derivative of e^{xln(a}) ?
The derivative of e^{xln(a}) is a^xln(a)
What is the first derivative of e^{xln(a}) ?
The first derivative of e^{xln(a}) is a^xln(a)