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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

Popular Examples

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\frac{d ^{2}}{d x ^{2}} (cos (x^{2}))

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\int - x^{5} sin (x) d x

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x \to 0 lim (500)

(\partial)/(\partial x)((4x^3y^4+9)^2)

\frac{\partial}{\partial x} ((4 x^{3} y^{4} + 9)^{2})

integral from-3 to 5 of |x|

\int_{- 3}^{5} ∣ x ∣ d x

Frequently Asked Questions (FAQ)

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