What is the derivative of 1/(y^2)*(y*x+x^2) ?

The derivative of 1/(y^2)*(y*x+x^2) is (-2x^2-xy)/(y^3)

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

The first derivative of 1/(y^2)*(y*x+x^2) is (-2x^2-xy)/(y^3)

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derivative of

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{y ^{2}}, g = y x + x^{2}

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

\frac{d}{d y} (\frac{1}{y ^{2}}) = - \frac{2}{y ^{3}}

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

= (- \frac{2}{y ^{3}}) (y x + x^{2}) + x \frac{1}{y ^{2}}

Simplify

(- \frac{2}{y ^{3}}) (y x + x^{2}) + x \frac{1}{y ^{2}} : \frac{- 2 x ^{2} - x y}{y ^{3}}

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

\int 2 r^{2} d r

x cos (1 - e^{x})

\int (\frac{7}{x ^{5}} + 4 x + 3) d x

ln (x x)

18 x - 3 x

What is the derivative of 1/(y^2)*(y*x+x^2) ?
The derivative of 1/(y^2)*(y*x+x^2) is (-2x^2-xy)/(y^3)
What is the first derivative of 1/(y^2)*(y*x+x^2) ?
The first derivative of 1/(y^2)*(y*x+x^2) is (-2x^2-xy)/(y^3)