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

The answer to (\partial)/(\partial x)(3x^2y-x+2y^3) is 6xy-1

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

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

6 x y - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 6 y x - 1 + 0

Simplify

= 6 x y - 1

2 x^{3} - 4 x^{2}

\int cos (4 x) cos (8 x) d x

\frac{d}{d x} (\frac{6}{3 x ^{5}} + \frac{2}{5 x ^{2}} - \frac{7}{9 x})

(y^{2} - x^{2}) d x + (- 2 x y) d y = 0

y^{^{''}} - 4 y^{^{'}} - 12 y = 8 e^{- 2 x}

What is (\partial)/(\partial x)(3x^2y-x+2y^3) ?
The answer to (\partial)/(\partial x)(3x^2y-x+2y^3) is 6xy-1