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Popular >

derivative of ((4x+b)/((cx+d)))

Solution

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

Solution

\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}}

Graph

Popular Examples

xy+(dy)/(dx)=100x

x y + \frac{d y}{d x} = 100 x

(dy)/(dx)+8y=e^xy^{-8}

\frac{d y}{d x} + 8 y = e^{x} y^{- 8}

limit as x approaches 5-of 4x-5

x \to 5 - lim (4 x - 5)

integral of x/((x-1)(x+2))

\int \frac{x}{( x - 1 ) ( x + 2 )} d x

integral of ((5x^2+8x+5))/((x-5)(x^2+9))

\int \frac{( 5 x ^{2} + 8 x + 5 )}{( x - 5 ) ( x ^{2} + 9 )} d x

Frequently Asked Questions (FAQ)

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)