What is (\partial)/(\partial x)(y/(x^2(y+3))) ?

The answer to (\partial)/(\partial x)(y/(x^2(y+3))) is -(2y)/(x^3(y+3))

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(\partial)/(\partial x)(y/(x^2(y+3)))

\frac{\partial}{\partial x} (\frac{y}{x ^{2} ( y + 3 )})

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

Solution steps

\frac{\partial}{\partial x} (\frac{y}{x ^{2} ( y + 3 )})

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

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

\int (sin (x) + 3) d x

\int e^{6}

y = cos (4 x)

\int \frac{1 - 2 x}{x ^{2}} d x

What is (\partial)/(\partial x)(y/(x^2(y+3))) ?
The answer to (\partial)/(\partial x)(y/(x^2(y+3))) is -(2y)/(x^3(y+3))