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

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

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

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

2 y x + sin (y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x + sin (y)

f (x) = 7 x^{4} cot (x)

\frac{\partial}{\partial z} (- x z)

\int_{1}^{8} \frac{x ^{2} - 1}{x} d x

\frac{d}{d x} (y - x)

\int_{0}^{π} x \cdot sin (n x) d x

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