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

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

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(\partial)/(\partial x)(3/(xy^2))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

arctan (s) + 1

x \to 0 lim (x - sin (x))

(6 x y^{2} - 3) d x + (6 x^{2} y + 4) d y = 0

\int \frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} d x

\frac{d}{d x} (\frac{6 x ^{3}}{3 x ^{2} - 3})

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