What is the derivative of (f(x))/(g(x)) ?

The derivative of (f(x))/(g(x)) is 1/g

What is the first derivative of (f(x))/(g(x)) ?

The first derivative of (f(x))/(g(x)) is 1/g

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derivative of

\frac{f ( x )}{g ( x )}

\frac{1}{g}

Solution steps

\frac{d}{df} (\frac{f x}{gx})

Treat

x, g

as constants

Take the constant out:

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

= \frac{x}{gx} \frac{df}{df}

Apply the common derivative:

\frac{df}{df} = 1

= \frac{x}{gx} \cdot 1

Simplify

\frac{x}{gx} \cdot 1 : \frac{1}{g}

= \frac{1}{g}

What is the derivative of (f(x))/(g(x)) ?
The derivative of (f(x))/(g(x)) is 1/g
What is the first derivative of (f(x))/(g(x)) ?
The first derivative of (f(x))/(g(x)) is 1/g