What is the first derivative of x/y ?

The first derivative of x/y is 1/y

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derivative of x/y

derivative of

\frac{x}{y}

\frac{1}{y}

Solution steps

\frac{d}{d x} (\frac{x}{y})

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= \frac{1}{y} \cdot 1

Simplify

= \frac{1}{y}

\int \frac{1}{( x ^{2} - 144 ) ^{\frac{3}{2}}} d x

\frac{d y}{d x} = 6 y^{\frac{2}{3}}

\int \frac{ln ( x )}{81} d x

\int x^{3} e^{- 2 x^{2}} d x

x y^{^{'}} + y = 2 e^{2 x}