What is (\partial)/(\partial x)(cos(xy)y) ?

The answer to (\partial)/(\partial x)(cos(xy)y) is -y^2sin(xy)

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(\partial)/(\partial x)(cos(xy)y)

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

- y^{2} sin (x y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y (- sin (x y) y)

Simplify

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

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

\frac{d}{d x} (sin^{c o s (x)} (x))

\int x sin (x) + 1 d x

\int_{2}^{4} (x - 2) d x

d er i v a t i v e cos (6 x)

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

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