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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

= 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

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

Simplify

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

n = 0 \sum \infty \frac{n !}{10 0 ^{n}}

\frac{d y}{d x} = 15 x y

\frac{\partial}{\partial x} (e^{- 2 x} cos (θ))

x \to 0 lim (1 - \frac{sin ( x )}{x})

\frac{d}{d x} (\frac{2 x ^{2}}{∣ x ∣})

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