What is the derivative of (f(x))^{g(x)} ?

The derivative of (f(x))^{g(x)} is gx(fx)^{gx-1}x

What is the first derivative of (f(x))^{g(x)} ?

The first derivative of (f(x))^{g(x)} is gx(fx)^{gx-1}x

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derivative of

(f (x))^{g (x)}

gx (f x)^{gx - 1} x

Solution steps

\frac{d}{df} ((f x)^{gx})

Treat

x, g

as constants

Apply the chain rule:

gx (f x)^{gx - 1} \frac{d}{df} (f x)

= gx (f x)^{gx - 1} \frac{d}{df} (f x)

\frac{d}{df} (f x) = x

= gx (f x)^{gx - 1} x

e^{- \frac{x}{2}} 0

f (x) = ln (x + x^{2} + 1)

\frac{d}{d x} (x^{2} sin (x) + 2)

\int (7 + e) d x

What is the derivative of (f(x))^{g(x)} ?
The derivative of (f(x))^{g(x)} is gx(fx)^{gx-1}x
What is the first derivative of (f(x))^{g(x)} ?
The first derivative of (f(x))^{g(x)} is gx(fx)^{gx-1}x