What is (\partial)/(\partial x)(x^2sin(xy)) ?

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

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(\partial)/(\partial x)(x^2sin(xy))

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

2 x sin (x y) + cos (x y) y x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = sin (x y)

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

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

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

= 2 x sin (x y) + cos (x y) y x^{2}

n = 0 \sum \infty 9^{n} x^{n}

9 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}

\int - 2 x 8 - x^{2} d x

x \to 0 + lim (\frac{x - ∣ x ∣}{x})

e^{x + 1}

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