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

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

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

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

3 x^{2} - 5 y

Solution steps

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

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

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

= 3 x^{2} - 5 y

\frac{x d y}{d x} + (3 x + 1) y = e^{- 3 x}

\int \frac{8 x}{( 2 x ^{2} + 5 ) ^{4}} d x

x \to 0 lim (\frac{sin ( 5 x )}{tan ( 6 x )})

\int \frac{1}{x ( 4 - ln ^{2} ( x ) )} d x

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