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Popular >

derivative of x/((y+1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of x/((y+1)) ?
The derivative of x/((y+1)) is (y+1-x\frac{dy)/(dx)}{(y+1)^2}
What is the first derivative of x/((y+1)) ?
The first derivative of x/((y+1)) is (y+1-x\frac{dy)/(dx)}{(y+1)^2}