What is (\partial)/(\partial x)(-2(y+1)x^{-3}) ?

The answer to (\partial)/(\partial x)(-2(y+1)x^{-3}) is (6(y+1))/(x^4)

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(\partial)/(\partial x)(-2(y+1)x^{-3})

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

\frac{6 ( y + 1 )}{x ^{4}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

- 2 (y + 1) (- 3 x^{- 3 - 1}) : \frac{6 ( y + 1 )}{x ^{4}}

= \frac{6 ( y + 1 )}{x ^{4}}

sin^{2} (x) - cos^{2} (x)

2 sin (x) y^{^{'}} + y cos (x) = y^{2} cos (x)

\frac{\partial}{\partial s} (r sin (t) sin (s))

\frac{\partial}{\partial x} (\frac{4 x - y}{4 x + y})

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

What is (\partial)/(\partial x)(-2(y+1)x^{-3}) ?
The answer to (\partial)/(\partial x)(-2(y+1)x^{-3}) is (6(y+1))/(x^4)