Check the solution to "Find the derivatives of the functions w=(2x−7)−1(x+5)" - Plainmath

Burhan Hopper

Answered question

2021-10-23

Find the derivatives of the functions

w = {(2 x - 7)}^{- 1} (x + 5)

Answer & Explanation

hajavaF

Skilled2021-10-24Added 90 answers

Step 1
Explanation:
Given that,

w = {(2 x - 7)}^{- 1} (x + 5)

Formula used:
According to the product rule of derivative:

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

Step 2
Calculation:

w = {(2 x - 7)}^{- 1} (x + 5)

Find the derivative separately first

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

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

\frac{d}{d x} (x + 5) = 1 + 0

=1
Now apply the product rule of derivative

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

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

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

= \frac{- 2 x - 10 + 2 x - 7}{{(2 x - 7)}^{2}}

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

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