What is the derivative of f(g(x)) ?

The derivative of f(g(x)) is gx

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

The first derivative of f(g(x)) is gx

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derivative of

f (g (x))

gx

Solution steps

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

Treat

g, x

as constants

Take the constant out:

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

= gx \frac{df}{df}

Apply the common derivative:

\frac{df}{df} = 1

= gx \cdot 1

Simplify

= gx

\frac{\partial}{\partial x} (x^{y^{z}})

f (x) = 7 x + 1, at x = 5

2 sin (2 x - π), 5 sin (2 x - 3 π)

\int \frac{1}{( 5 + x ) ^{2}} d x

\frac{d}{d x} (\frac{x ^{2}}{( x - 1 )})