Answered: "Find the derivatives of the functions y =..."

College
Calculus and Analysis
Differential Calculus
Derivatives

Suman Cole

Answered question

2021-10-07

Find the derivatives of the functions y = 2x + 5/3x - 2

Answer & Explanation

krolaniaN

Skilled2021-10-08Added 86 answers

Step 1
Given:
$y = \frac{2 x + 5}{3 x - 2}$
Step 2
Differentiate with respect to 'x':
$\frac{d y}{d x} = \frac{d}{d x} (\frac{2 x + 5}{3 x - 2})$
Apply the Quotient Rule: ${(\frac{f}{g})}^{'} = \frac{g \cdot f^{'} - f \cdot g^{'}}{g^{2}}$
Here f=2x+5, g=3x-2
$\frac{d y}{d x} = \frac{(3 x - 2) \frac{d}{d x} (2 x + 5) - (2 x + 5) \frac{d}{d x} (3 x - 2)}{{(3 x - 2)}^{2}}$

$\frac{d y}{d x} = \frac{2 (3 x - 2) - 3 (2 x + 5)}{{(3 x - 2)}^{2}}$

$\frac{d y}{d x} = \frac{- 6 x - 4 - 6 x - 15}{{(3 x - 2)}^{2}}$

$\frac{d y}{d x} = - \frac{19}{{(3 x - 2)}^{2}}$

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