What is the derivative of a^xln(a) ?

The derivative of a^xln(a) is a^xln^2(a)

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

The first derivative of a^xln(a) is a^xln^2(a)

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

a^{x} ln^{2} (a)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the derivative exponent rule:

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

= ln (a) a^{x} ln (a)

Simplify

ln (a) a^{x} ln (a) : a^{x} ln^{2} (a)

= a^{x} ln^{2} (a)

f (x) = - 5 x + 2

x \to 0 lim (\frac{sin ( x ^{6} )}{x})

\int_{0}^{2} 3 e^{- 2 x} d x

\frac{d}{d x} (x^{5} - 5 x^{3} + 4 x)

e^{8 x^{2}}

What is the derivative of a^xln(a) ?
The derivative of a^xln(a) is a^xln^2(a)
What is the first derivative of a^xln(a) ?
The first derivative of a^xln(a) is a^xln^2(a)