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

The answer to (\partial)/(\partial x)((y)(sin(z)x-x)) is y(sin(z)-1)

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(\partial)/(\partial x)((y)(sin(z)x-x))

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

y (sin (z) - 1)

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (sin (z) x) = sin (z)

\frac{\partial}{\partial x} (x) = 1

= y (sin (z) - 1)

x (x^{3 + \frac{2}{x}})

a (e^{- k a^{2}} - 2 k e^{- k a^{2}} a^{2})

(4 x^{3} \circ 2 x - 3) (x)

(- 1 + 6 x) - 7 + 5

(\frac{3}{e ^{q}} + 10) \cdot q

What is (\partial)/(\partial x)((y)(sin(z)x-x)) ?
The answer to (\partial)/(\partial x)((y)(sin(z)x-x)) is y(sin(z)-1)