What is the derivative of (x-3/(x-4)) ?

The derivative of (x-3/(x-4)) is -1/((x-4)^2)

What is the first derivative of (x-3/(x-4)) ?

The first derivative of (x-3/(x-4)) is -1/((x-4)^2)

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\frac{d}{d x} (\frac{x - 3}{x - 4})

- \frac{1}{( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 3}{x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 3 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x - 3 )}{( x - 4 ) ^{2}}

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (x - 4) = 1

= \frac{1 \cdot ( x - 4 ) - 1 \cdot ( x - 3 )}{( x - 4 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 4 ) - 1 \cdot ( x - 3 )}{( x - 4 ) ^{2}} : - \frac{1}{( x - 4 ) ^{2}}

= - \frac{1}{( x - 4 ) ^{2}}

\frac{d}{d x} (e^{x} - π)

\int \frac{x ^{2}}{16 + x ^{2}} d x

\frac{1}{x}, x, \frac{1}{4} x

\int \frac{5 x}{x ^{2} + 4 x + 4} d x

f (x) = \frac{1}{3 - 2 x}

What is the derivative of (x-3/(x-4)) ?
The derivative of (x-3/(x-4)) is -1/((x-4)^2)
What is the first derivative of (x-3/(x-4)) ?
The first derivative of (x-3/(x-4)) is -1/((x-4)^2)