What is the derivative of x/(x-37) ?

The derivative of x/(x-37) is -(37)/((x-37)^2)

What is the first derivative of x/(x-37) ?

The first derivative of x/(x-37) is -(37)/((x-37)^2)

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\frac{d}{d x} (\frac{x}{x - 37})

- \frac{37}{( x - 37 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 37})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x - 37 ) - \frac{d}{d x} ( x - 37 ) x}{( x - 37 ) ^{2}}

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

\frac{d}{d x} (x - 37) = 1

= \frac{1 \cdot ( x - 37 ) - 1 \cdot x}{( x - 37 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 37 ) - 1 \cdot x}{( x - 37 ) ^{2}} : - \frac{37}{( x - 37 ) ^{2}}

= - \frac{37}{( x - 37 ) ^{2}}

f (x) = sin (3 x^{2})

\int \frac{1}{20} d x

f (x) = e^{x^{2}}

\int - sin^{3} (x) d x

\int \frac{4}{cos ( x ) - 1} d x

What is the derivative of x/(x-37) ?
The derivative of x/(x-37) is -(37)/((x-37)^2)
What is the first derivative of x/(x-37) ?
The first derivative of x/(x-37) is -(37)/((x-37)^2)