What is the derivative of ((x+2))/((y-2)) ?

The derivative of ((x+2))/((y-2)) is 1/(y-2)

What is the first derivative of ((x+2))/((y-2)) ?

The first derivative of ((x+2))/((y-2)) is 1/(y-2)

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derivative of

\frac{( x + 2 )}{( y - 2 )}

\frac{1}{y - 2}

Solution steps

\frac{d}{d x} (\frac{x + 2}{y - 2})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{y - 2} \frac{d}{d x} (x + 2)

Apply the Sum/Difference Rule:

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

= \frac{1}{y - 2} (\frac{d x}{d x} + \frac{d}{d x} (2))

\frac{d x}{d x} = 1

\frac{d}{d x} (2) = 0

= \frac{1}{y - 2} (1 + 0)

Simplify

= \frac{1}{y - 2}

What is the derivative of ((x+2))/((y-2)) ?
The derivative of ((x+2))/((y-2)) is 1/(y-2)
What is the first derivative of ((x+2))/((y-2)) ?
The first derivative of ((x+2))/((y-2)) is 1/(y-2)