What is the derivative of (2x^2)/((x^2+y^2)) ?

The derivative of (2x^2)/((x^2+y^2)) is (4xy^2)/((x^2+y^2)^2)

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

The first derivative of (2x^2)/((x^2+y^2)) is (4xy^2)/((x^2+y^2)^2)

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derivative of

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{2 x ( x ^{2} + y ^{2} ) - 2 x x ^{2}}{( x ^{2} + y ^{2} ) ^{2}} : \frac{4 x y ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

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

(x + 2)^{2} \cdot (x - 3)^{3}

\frac{q}{2}

\frac{d}{d x} (\frac{( 1 - cos ( x y ) )}{x})

\frac{d}{d x} (\frac{( 5 + 4 - x )}{6})

f (x) = cos (x^{3}) sin^{2} (x^{5})

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