What is (\partial)/(\partial x)(((3x-3z))/(y+3z)) ?

The answer to (\partial)/(\partial x)(((3x-3z))/(y+3z)) is 3/(y+3z)

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(\partial)/(\partial x)(((3x-3z))/(y+3z))

\frac{\partial}{\partial x} (\frac{( 3 x - 3 z )}{y + 3 z})

\frac{3}{y + 3 z}

Solution steps

\frac{\partial}{\partial x} (\frac{( 3 x - 3 z )}{y + 3 z})

Treat

z, y

as constants

Take the constant out:

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

= \frac{1}{y + 3 z} \frac{\partial}{\partial x} (3 x - 3 z)

Apply the Sum/Difference Rule:

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

= \frac{1}{y + 3 z} (\frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (3 z))

\frac{\partial}{\partial x} (3 x) = 3

\frac{\partial}{\partial x} (3 z) = 0

= \frac{1}{y + 3 z} (3 - 0)

Simplify

\frac{1}{y + 3 z} (3 - 0) : \frac{3}{y + 3 z}

= \frac{3}{y + 3 z}

\int 3 cos (x) - 2 sin (x) d x

t an g e n t e^{x} + 1, at x = 0

a re a y = 3 + 2 x, y = \frac{9 + x}{3}

t an g e n t y = - 2 x^{3}, (- 2, 16)

\int \frac{2 y}{3} d y

What is (\partial)/(\partial x)(((3x-3z))/(y+3z)) ?
The answer to (\partial)/(\partial x)(((3x-3z))/(y+3z)) is 3/(y+3z)