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

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

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

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

1 + \frac{1}{y - z}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 1 + \frac{1}{y - z}

\frac{d}{d x} (tan (cos (\frac{x}{2})))

\int e^{x^{3} + 5} \cdot x^{2} d x

\int \frac{8 - e ^{x}}{e ^{5 x}} d x

x \to 2 lim (x - 1 - 2 x)

3^{x} tan (ln (x))

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