What is (\partial)/(\partial y)(x^{-7}y^2+xy^2+3xy) ?

The answer to (\partial)/(\partial y)(x^{-7}y^2+xy^2+3xy) is (2y)/(x^7)+2xy+3x

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(\partial)/(\partial y)(x^{-7}y^2+xy^2+3xy)

\frac{\partial}{\partial y} (x^{- 7} y^{2} + x y^{2} + 3 x y)

\frac{2 y}{x ^{7}} + 2 x y + 3 x

Solution steps

\frac{\partial}{\partial y} (x^{- 7} y^{2} + x y^{2} + 3 x y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (x^{- 7} y^{2}) + \frac{\partial}{\partial y} (x y^{2}) + \frac{\partial}{\partial y} (3 x y)

\frac{\partial}{\partial y} (x^{- 7} y^{2}) = \frac{2 y}{x ^{7}}

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

\frac{\partial}{\partial y} (3 x y) = 3 x

= \frac{2 y}{x ^{7}} + 2 x y + 3 x

\frac{d y}{d x} = - 10 y, y (0) = 5

\int_{0}^{\frac{1}{2}} 8 x (\frac{1}{2} - x) d x

\frac{\partial}{\partial x} (x \cdot sin (x) - 1)

n = 1 \sum \infty n e^{- \frac{n}{2}}

\int \frac{4 x + 2}{x ^{2}} d x

What is (\partial)/(\partial y)(x^{-7}y^2+xy^2+3xy) ?
The answer to (\partial)/(\partial y)(x^{-7}y^2+xy^2+3xy) is (2y)/(x^7)+2xy+3x