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

The answer to (\partial)/(\partial x)(2x^3+3y^2-5xy) is 6x^2-5y

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

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

6 x^{2} - 5 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

= 6 x^{2} + 0 - 5 y

Simplify

= 6 x^{2} - 5 y

What is (\partial)/(\partial x)(2x^3+3y^2-5xy) ?
The answer to (\partial)/(\partial x)(2x^3+3y^2-5xy) is 6x^2-5y