Question: "Find the derivatives of the functions y=(2x-5)(4-x)-1" - Plainmath

Jessie Lee

Answered question

2021-12-07

Find the derivatives of the functions y=(2x-5)(4-x)-1

Answer & Explanation

sukljama2

Beginner2021-12-08Added 32 answers

Step 1
To find the derivative of the function,
y=(2x-5)(4-x)-1
Step 2
Given,
y=(2x-5)(4-x)-1
Differentiating with respect to x,

\Rightarrow \frac{d y}{d x} = \frac{d [(2 x - 5) (4 - x)]}{d x} - \frac{d (1)}{d x}

\Rightarrow \frac{d y}{d x} = (2 x - 5) \frac{d (4 - x)}{d x} + (4 - x) \frac{d (2 x - 5)}{d x} - 0

\Rightarrow \frac{d y}{d x} = (2 x - 5) (- 1) + (4 - x) (2)

\Rightarrow \frac{d y}{d x} = - 2 x + 5 + 8 - 2 x

∴ \frac{d y}{d x} = 13 - 4 x

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