What is (\partial)/(\partial x)(2x^3y-3y^2z) ?

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

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(\partial)/(\partial x)(2x^3y-3y^2z)

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

6 x^{2} y

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 6 y x^{2} - 0

Simplify

= 6 x^{2} y

d er i v a t i v e 2 4 - x

\frac{d}{d x} (ka ln (\frac{x + d}{x - d}))

t a y l or \frac{1}{2} cos (7 x)

\frac{d y}{d x} = y^{2} + 2 y

\frac{\partial}{\partial x} (e^{i x})

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