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

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

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

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

(2 + x) y^{^{'}} = 5 y

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

\frac{1}{1 - x + \frac{x ^{2}}{2}}, 0

\frac{d}{d x} (\frac{4 x ^{2} tan ( x )}{sec ( x )})

\frac{d}{d x} (x^{8} (x - 1)^{7})

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