What is (\partial)/(\partial y)(x^3+ky^2-5xy) ?

The answer to (\partial)/(\partial y)(x^3+ky^2-5xy) is 2ky-5x

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(\partial)/(\partial y)(x^3+ky^2-5xy)

\frac{\partial}{\partial y} (x^{3} + k y^{2} - 5 x y)

2 k y - 5 x

Solution steps

\frac{\partial}{\partial y} (x^{3} + k y^{2} - 5 x y)

Treat

k, x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{3}) + \frac{\partial}{\partial y} (k y^{2}) - \frac{\partial}{\partial y} (5 x y)

\frac{\partial}{\partial y} (x^{3}) = 0

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

\frac{\partial}{\partial y} (5 x y) = 5 x

= 0 + 2 k y - 5 x

Simplify

= 2 k y - 5 x

\frac{d}{d x} ((x^{2} - 7)^{2})

y = - \frac{8 x}{x ^{2} + 1}

f (x) = \frac{e ^{x}}{x + 6}, (0, \frac{1}{6})

f (x) = (x + 2 x) e^{x}

\int \frac{13}{13 + e ^{x}} d x

What is (\partial)/(\partial y)(x^3+ky^2-5xy) ?
The answer to (\partial)/(\partial y)(x^3+ky^2-5xy) is 2ky-5x