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

The derivative of {f}(x({g}(x))) is derivative of {f}(x){g}(x)+derivative of {g}(x){f}(x)

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

The first derivative of {f}(x({g}(x))) is derivative of {f}(x){g}(x)+derivative of {g}(x){f}(x)

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\frac{d}{d x} (f (x) (g (x)))

\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

Solution steps

\frac{d}{d x} (f (x) (g (x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (x), g = g (x)

= \frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

= \frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x)

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