What is (\partial)/(\partial x)(x^3-15xy+y^3) ?

The answer to (\partial)/(\partial x)(x^3-15xy+y^3) is 3x^2-15y

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(\partial)/(\partial x)(x^3-15xy+y^3)

\frac{\partial}{\partial x} (x^{3} - 15 x y + y^{3})

3 x^{2} - 15 y

Solution steps

\frac{\partial}{\partial x} (x^{3} - 15 x y + y^{3})

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

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

\frac{\partial}{\partial x} (15 x y) = 15 y

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

= 3 x^{2} - 15 y + 0

Simplify

= 3 x^{2} - 15 y

x^{3}, 2 x - 12.3 x^{2}

\frac{d}{d x} (arctan (\frac{1}{10 x}) + 1)

\frac{3 x ^{2} - 4 x + 1}{x ^{3} + 1}

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

f (x) = x^{3} - 2 x^{2}, g (x) = x^{2} - 2 x

What is (\partial)/(\partial x)(x^3-15xy+y^3) ?
The answer to (\partial)/(\partial x)(x^3-15xy+y^3) is 3x^2-15y