What is the derivative of (2x-7^{-1}(x+5)) ?

The derivative of (2x-7^{-1}(x+5)) is -(17)/((2x-7)^2)

What is the first derivative of (2x-7^{-1}(x+5)) ?

The first derivative of (2x-7^{-1}(x+5)) is -(17)/((2x-7)^2)

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\frac{d}{d x} ((2 x - 7)^{- 1} (x + 5))

- \frac{17}{( 2 x - 7 ) ^{2}}

Solution steps

\frac{d}{d x} ((2 x - 7)^{- 1} (x + 5))

Apply the Product Rule:

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

f = (2 x - 7)^{- 1}, g = x + 5

= \frac{d}{d x} ((2 x - 7)^{- 1}) (x + 5) + \frac{d}{d x} (x + 5) (2 x - 7)^{- 1}

\frac{d}{d x} ((2 x - 7)^{- 1}) = - \frac{2}{( 2 x - 7 ) ^{2}}

\frac{d}{d x} (x + 5) = 1

= (- \frac{2}{( 2 x - 7 ) ^{2}}) (x + 5) + 1 \cdot (2 x - 7)^{- 1}

Simplify

(- \frac{2}{( 2 x - 7 ) ^{2}}) (x + 5) + 1 \cdot (2 x - 7)^{- 1} : - \frac{17}{( 2 x - 7 ) ^{2}}

= - \frac{17}{( 2 x - 7 ) ^{2}}

What is the derivative of (2x-7^{-1}(x+5)) ?
The derivative of (2x-7^{-1}(x+5)) is -(17)/((2x-7)^2)
What is the first derivative of (2x-7^{-1}(x+5)) ?
The first derivative of (2x-7^{-1}(x+5)) is -(17)/((2x-7)^2)