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

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

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

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

3 x^{2} - 5 y

Solution steps

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

Treat

k, y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (k y^{2}) = 0

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

= 3 x^{2} + 0 - 5 y

Simplify

= 3 x^{2} - 5 y

\int 3 x 1 - x^{2} d x

4 x y^{^{'}} = 2 x e^{x} - 4 y + 6 x^{2}

\int x sin^{3} (x^{2}) cos (x^{2}) d x

\frac{d y}{d x} = x, y (11) = 5

y = 5 sec (x), at x = \frac{π}{3}

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