What is the derivative of (2x-5^{-1}*(4x+3)^{-1}) ?

The derivative of (2x-5^{-1}*(4x+3)^{-1}) is (-16x+14)/((2x-5)^2(4x+3)^2)

What is the first derivative of (2x-5^{-1}*(4x+3)^{-1}) ?

The first derivative of (2x-5^{-1}*(4x+3)^{-1}) is (-16x+14)/((2x-5)^2(4x+3)^2)

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\frac{d}{d x} ((2 x - 5)^{- 1} \cdot (4 x + 3)^{- 1})

\frac{- 16 x + 14}{( 2 x - 5 ) ^{2} ( 4 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} ((2 x - 5)^{- 1} (4 x + 3)^{- 1})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (2 x - 5)^{- 1}, g = (4 x + 3)^{- 1}

= \frac{d}{d x} ((2 x - 5)^{- 1}) (4 x + 3)^{- 1} + \frac{d}{d x} ((4 x + 3)^{- 1}) (2 x - 5)^{- 1}

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

\frac{d}{d x} ((4 x + 3)^{- 1}) = - \frac{4}{( 4 x + 3 ) ^{2}}

= (- \frac{2}{( 2 x - 5 ) ^{2}}) (4 x + 3)^{- 1} + (- \frac{4}{( 4 x + 3 ) ^{2}}) (2 x - 5)^{- 1}

Simplify

(- \frac{2}{( 2 x - 5 ) ^{2}}) (4 x + 3)^{- 1} + (- \frac{4}{( 4 x + 3 ) ^{2}}) (2 x - 5)^{- 1} : \frac{- 16 x + 14}{( 2 x - 5 ) ^{2} ( 4 x + 3 ) ^{2}}

= \frac{- 16 x + 14}{( 2 x - 5 ) ^{2} ( 4 x + 3 ) ^{2}}

\int_{0}^{3} \frac{9 e ^{9 x}}{1 + e ^{9 x}} d x

f (s 0) = s - 3 (s 2 + 4 s + 13)

\int \frac{1}{x ^{5} + 16 x ^{3} + 64 x} d x

3 x + 7, at x = 3

x \to 2 lim (6 x + 1)

What is the derivative of (2x-5^{-1}*(4x+3)^{-1}) ?
The derivative of (2x-5^{-1}*(4x+3)^{-1}) is (-16x+14)/((2x-5)^2(4x+3)^2)
What is the first derivative of (2x-5^{-1}*(4x+3)^{-1}) ?
The first derivative of (2x-5^{-1}*(4x+3)^{-1}) is (-16x+14)/((2x-5)^2(4x+3)^2)