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Popular >

derivative of a^{{f}(x})

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

a^{f (x)} = e^{f (x) l n (a)}

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

Apply the chain rule:

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

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

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

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

e^{f (x) l n (a)} = a^{f (x)}

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

Popular Examples

integral of e^{-θ}cos(2θ)

\int e^{- θ} cos (2 θ) d θ

integral of (19arctan(x))/(x^2)

\int \frac{19 arctan ( x )}{x ^{2}} d x

limit as x approaches 0 of ((x+1)^3-1)/x

x \to 0 lim (\frac{( x + 1 ) ^{3} - 1}{x})

slope of 1/(x-3)slope

\frac{1}{x - 3}

(\partial}{\partial x}(\frac{s-2r)/t)

\frac{\partial}{\partial x} (\frac{s - 2 r}{t})

Frequently Asked Questions (FAQ)

What is the derivative of a^{{f}(x}) ?
The derivative of a^{{f}(x}) is a^{{f}(x)}ln(a) derivative of {f}(x)
What is the first derivative of a^{{f}(x}) ?
The first derivative of a^{{f}(x}) is a^{{f}(x)}ln(a) derivative of {f}(x)