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

The answer to (\partial)/(\partial x)(z^2cos(yx)) is -z^2ysin(yx)

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(\partial)/(\partial x)(z^2cos(yx))

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{'}} - \frac{6}{x} y = \frac{( y ^{3} )}{x ^{4}}

\int_{4}^{9} x x d x

\int \frac{1}{x ^{2} x ^{2} - 196} d x

\int \frac{e ^{x} ( 2 x ^{3} + x ^{2} - 4 x - 6 )}{6 x ^{4}} d x

t \to 0 lim (\frac{sin ( 2 t )}{t})

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