What is (\partial)/(\partial x)(sin(z)cos(xy)) ?

The answer to (\partial)/(\partial x)(sin(z)cos(xy)) is -ysin(xy)sin(z)

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(\partial)/(\partial x)(sin(z)cos(xy))

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

- y sin (x y) sin (z)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

= sin (z) \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

= sin (z) (- sin (x y) y)

Simplify

= - y sin (x y) sin (z)

x \to 0 lim (\frac{x ^{3} + 5 x}{x})

\int_{0}^{x} \frac{1}{t ^{2} - 25} d t

y^{^{'}} = y + 3 t e^{t}, y (0) = 4

x \to 3 lim (x - 8)

\int (s^{3} + 3)^{2} (1 - s^{2})^{3} d s

What is (\partial)/(\partial x)(sin(z)cos(xy)) ?
The answer to (\partial)/(\partial x)(sin(z)cos(xy)) is -ysin(xy)sin(z)