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

The answer to (\partial)/(\partial x)(3x^2y+xsin(2y)) is 6yx+sin(2y)

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

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

6 y x + sin (2 y)

Solution steps

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

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 sin (2 y))

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

\frac{\partial}{\partial x} (x sin (2 y)) = sin (2 y)

= 6 y x + sin (2 y)

y^{^{'}} = \frac{3 y ^{2} - x ^{2}}{2 x y}

y^{^{'}} + sin (t) y = - sin (t), y (0) = 7

\frac{\partial}{\partial x} (\frac{1}{4} x^{a} y^{1 - a})

\int e^{- 2} d x

4 x - 12, [2, 6]

What is (\partial)/(\partial x)(3x^2y+xsin(2y)) ?
The answer to (\partial)/(\partial x)(3x^2y+xsin(2y)) is 6yx+sin(2y)