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Popular >

derivative of x/((x+1))

Solution

\frac{d}{d 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}}

Graph

Popular Examples

d/(dk)(ln(3+k))

\frac{d}{d k} (ln (3 + k))

derivative of (x+(x+sin^2(x)^3)^4)

\frac{d}{d x} ((x + (x + sin^{2} (x))^{3})^{4})

integral of 3x+x/((x^2+2)^{4/3)}

\int 3 x + \frac{x}{( x ^{2} + 2 ) ^{\frac{4}{3}}} d x

derivative of y=x^{2/3}-x derivative of

y = x^{\frac{2}{3}} - x

derivative of x^2-2x^2

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

Frequently Asked Questions (FAQ)

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