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Popular >

derivative of (6x-1/(4x+5))

Solution

\frac{d}{d x} (\frac{6 x - 1}{4 x + 5})

Solution

\frac{34}{( 4 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x - 1}{4 x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x - 1 ) ( 4 x + 5 ) - \frac{d}{d x} ( 4 x + 5 ) ( 6 x - 1 )}{( 4 x + 5 ) ^{2}}

\frac{d}{d x} (6 x - 1) = 6

\frac{d}{d x} (4 x + 5) = 4

= \frac{6 ( 4 x + 5 ) - 4 ( 6 x - 1 )}{( 4 x + 5 ) ^{2}}

Expand

6 (4 x + 5) - 4 (6 x - 1) : 34

= \frac{34}{( 4 x + 5 ) ^{2}}

Popular Examples

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\int \frac{1}{2 x + 3} d x

derivative of (1/2 x^2-3^2)

\frac{d}{d x} ((\frac{1}{2} x^{2} - 3)^{2})

x^2(dy)/(dx)=(x+1)y

x^{2} \frac{d y}{d x} = (x + 1) y

area y=xe^{-x},y=0,x=4 area

y = x e^{- x}, y = 0, x = 4

limit as x approaches+1 of (x^2-9)^{1/3}

x \to + 1 lim ((x^{2} - 9)^{\frac{1}{3}})

Frequently Asked Questions (FAQ)

What is the derivative of (6x-1/(4x+5)) ?
The derivative of (6x-1/(4x+5)) is (34)/((4x+5)^2)
What is the first derivative of (6x-1/(4x+5)) ?
The first derivative of (6x-1/(4x+5)) is (34)/((4x+5)^2)