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

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

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

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

3 x^{2} - 5 y

Solution steps

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

Treat

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

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

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

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

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

Simplify

= 3 x^{2} - 5 y

\frac{d}{d x} (\frac{4 + x}{1 - 4 x})

f (x) = x^{3} - 5 x + 3, at x = 3

f (x) = (- x^{2} - 4)^{2}

\frac{d}{d x} (3 x^{2} - \frac{1}{24} ln (x))

\int \frac{1}{x ^{2} + 4 x + 20} d x

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