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derivative of f(x)= x/(x+1)

Solution

derivative of

f (x) = \frac{x}{x + 1}

Solution

\frac{1}{( x + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Popular Examples

simplify (6.5)(2.7)simplify

(6.5) (2.7)

x = - 6

derivative of y=3sqrt(x)+2/(sqrt(x))derivative of

y = 3 x + \frac{2}{x}

derivative of y=6-5x^9+2x^8-2x^6 derivative of

y = 6 - 5 x^{9} + 2 x^{8} - 2 x^{6}

tangent of f(x)=(2x)/(3x-1),\at x=1 tangent of

f (x) = \frac{2 x}{3 x - 1}, at x = 1

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x+1) ?
The derivative of f(x)= x/(x+1) is 1/((x+1)^2)
What is the first derivative of f(x)= x/(x+1) ?
The first derivative of f(x)= x/(x+1) is 1/((x+1)^2)