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Popular >

d/(dy)((y^2)/(y^2+1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d y} (y^{2}) = 2 y

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

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

Simplify

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

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

Popular Examples

slope of (3,-3),(1,-1)slope

(3, - 3), (1, - 1)

(\partial)/(\partial x)(xe^{yz})

\frac{\partial}{\partial x} (x e^{yz})

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

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

integral from 0 to 0.5 of 400x

\int_{0}^{0.5} 400 x d x

tangent of f(x)=(1+2x)^{11},(0,1)tangent of

f (x) = (1 + 2 x)^{11}, (0, 1)

Frequently Asked Questions (FAQ)

What is the d/(dy)((y^2)/(y^2+1)) ?
The d/(dy)((y^2)/(y^2+1)) is (2y)/((y^2+1)^2)
What is the first d/(dy)((y^2)/(y^2+1)) ?
The first d/(dy)((y^2)/(y^2+1)) is (2y)/((y^2+1)^2)