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Popular Calculus >

derivative of (3x+4)/(3x-4)

Solution

derivative of

\frac{3 x + 4}{3 x - 4}

Solution

- \frac{24}{( 3 x - 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x + 4) = 3

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

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

Simplify

\frac{3 ( 3 x - 4 ) - 3 ( 3 x + 4 )}{( 3 x - 4 ) ^{2}} : - \frac{24}{( 3 x - 4 ) ^{2}}

= - \frac{24}{( 3 x - 4 ) ^{2}}

Graph

Popular Examples

x(y+1)dx+y(x-1)dy=0

x (y + 1) d x + y (x - 1) d y = 0

limit as x approaches 0 of x/(x^2-1)

x \to 0 lim (\frac{x}{x ^{2} - 1})

derivative of 1/(x(ln(x)))

\frac{d}{d x} (\frac{1}{x ( ln ( x ) )})

81y^{''}+108y^'+66y=0,y^'(0)=2,y(0)=6

81 y^{^{''}} + 108 y^{^{'}} + 66 y = 0, y^{^{'}} (0) = 2, y (0) = 6

tangent of sqrt(1-x)

t an g e n t 1 - x

Frequently Asked Questions (FAQ)

What is the derivative of (3x+4)/(3x-4) ?
The derivative of (3x+4)/(3x-4) is -(24)/((3x-4)^2)
What is the first derivative of (3x+4)/(3x-4) ?
The first derivative of (3x+4)/(3x-4) is -(24)/((3x-4)^2)