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

The answer to (\partial)/(\partial x)(x^2cos(xy)) is 2xcos(xy)-x^2ysin(xy)

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int x (3 sec^{2} (x) - tan^{2} (x)) d x

\int \frac{x}{x ^{2} + 6 x + 18} d x

\frac{s + 1}{s ( s ^{2} + 4 s + 4 )}

\frac{d}{d x} (x csc (x))

x^{3} + 2 x

What is (\partial)/(\partial x)(x^2cos(xy)) ?
The answer to (\partial)/(\partial x)(x^2cos(xy)) is 2xcos(xy)-x^2ysin(xy)