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

The derivative of y/(y+x^2) is (x^2\frac{dy)/(dx)-2xy}{(y+x^2)^2}

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Expand

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

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

\frac{d}{d x} (e^{x^{2}} sin (x))

\frac{d x}{d t} = 2 x (10 - x)

\frac{\partial}{\partial t} (e^{t} sin (t))

\frac{d}{d x} (3 ln (4 x))

\int_{1}^{3} (4 x - 3)^{2} - (x^{2})^{2} d x

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