What is the derivative of ((4x+b)/((cx+d))) ?

The derivative of ((4x+b)/((cx+d))) is (-bc+4d)/((cx+d)^2)

What is the first derivative of ((4x+b)/((cx+d))) ?

The first derivative of ((4x+b)/((cx+d))) is (-bc+4d)/((cx+d)^2)

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\frac{d}{d x} (\frac{( 4 x + b )}{( c x + d )})

\frac{- b c + 4 d}{( c x + d ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 4 x + b )}{( c x + d )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x + b ) ( c x + d ) - \frac{d}{d x} ( c x + d ) ( 4 x + b )}{( c x + d ) ^{2}}

\frac{d}{d x} (4 x + b) = 4

\frac{d}{d x} (c x + d) = c

= \frac{4 ( c x + d ) - c ( 4 x + b )}{( c x + d ) ^{2}}

Expand

4 (c x + d) - c (4 x + b) : - b c + 4 d

= \frac{- b c + 4 d}{( c x + d ) ^{2}}

What is the derivative of ((4x+b)/((cx+d))) ?
The derivative of ((4x+b)/((cx+d))) is (-bc+4d)/((cx+d)^2)
What is the first derivative of ((4x+b)/((cx+d))) ?
The first derivative of ((4x+b)/((cx+d))) is (-bc+4d)/((cx+d)^2)