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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

= 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

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

\int \frac{sin ( x )}{x} d x

\frac{\partial}{\partial x} (a x^{2} + b x + c)

\int_{0}^{1} \frac{1}{( 2 x - 3 ) ^{2}} d x

\frac{d}{d x} (\frac{192}{x ^{4}})

\frac{d}{d x} (sin^{2} (cos (4 x)))

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