What is (\partial)/(\partial x)(z^3cos(yx)) ?

The answer to (\partial)/(\partial x)(z^3cos(yx)) is -z^3ysin(yx)

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(\partial)/(\partial x)(z^3cos(yx))

\frac{\partial}{\partial x} (z^{3} cos (y x))

- z^{3} y sin (y x)

Solution steps

\frac{\partial}{\partial x} (z^{3} cos (y x))

Treat

z, y

as constants

Take the constant out:

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

= z^{3} \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^{3} (- sin (y x) y)

Simplify

= - z^{3} y sin (y x)

\frac{d ^{3}}{d x ^{3}} (3 x^{5} + x^{4})

\frac{3}{s + 2} \cdot \frac{1}{s}

y = x e^{- k x}

f (x) = x^{2} - 7

41 (6 t^{3} - 7)^{\frac{6}{5}}

What is (\partial)/(\partial x)(z^3cos(yx)) ?
The answer to (\partial)/(\partial x)(z^3cos(yx)) is -z^3ysin(yx)