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Popular >

derivative of f(x)= x/(x+4)

Solution

derivative of

f (x) = \frac{x}{x + 4}

Solution

\frac{4}{( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 4})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x + 4 ) - \frac{d}{d x} ( x + 4 ) x}{( x + 4 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x + 4) = 1

= \frac{1 \cdot ( x + 4 ) - 1 \cdot x}{( x + 4 ) ^{2}}

1 \cdot (x + 4) - 1 \cdot x = 4

= \frac{4}{( x + 4 ) ^{2}}

Popular Examples

integral of 1/((x-1)(x^2+3))

\int \frac{1}{( x - 1 ) ( x ^{2} + 3 )} d x

integral of ye^{xy}cos(2x)

\int y e^{x y} cos (2 x) d x

integral of 3t^2

\int 3 t^{2} d t

d/(d{z)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}})

\frac{d}{d z} (\frac{z}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

derivative of (sin(5x)(arccsc(2)x^3))

\frac{d}{d x} ((sin (5 x)) (arccsc (2) x^{3}))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x+4) ?
The derivative of f(x)= x/(x+4) is 4/((x+4)^2)
What is the first derivative of f(x)= x/(x+4) ?
The first derivative of f(x)= x/(x+4) is 4/((x+4)^2)