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Popular >

derivative of {f}(x{g}(x))

Solution

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

Solution

\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)

Popular Examples

derivative of y/(y+a/y)derivative of

\frac{y}{y + \frac{a}{y}}

sum from n=0 to infinity of n/(e^{2n)}

n = 0 \sum \infty \frac{n}{e ^{2 n}}

integral of (e^{4x}-e^{2x}+1)/(e^x)

\int \frac{e ^{4 x} - e ^{2 x} + 1}{e ^{x}} d x

y^{^{'}} = y

derivative of f(x)=4sqrt(x)-6 derivative of

f (x) = 4 x - 6

Frequently Asked Questions (FAQ)

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)