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Pearl Carney

Answered question

2021-12-03

Use the rules for derivatives to find the derivative of function defined as follows.

y = \frac{\ln | 2 x - 1 |}{x + 3}

Answer & Explanation

Opeance1951

Beginner2021-12-04Added 26 answers

Step 1
The given function is:

y = \frac{\ln | 2 x - 1 |}{x + 3}

To find the derivative of this function, apply the quotient rule,

\frac{d}{d x} (\frac{u}{v}) = \frac{v \frac{d}{d x} (u) - u \frac{d}{d x} (v)}{v^{2}}

Step 2
So,

\frac{d y}{d x} = \frac{d}{d x} (\frac{\ln | 2 x - 1 |}{x + 3})

\frac{d y}{d x} = \frac{(x + 3) \frac{d}{d x} (\ln | 2 x - 1 |) - (\ln | 2 x - 1 |) \frac{d}{d x} (x + 3)}{{(x + 3)}^{2}}

\frac{d y}{d x} = \frac{(x + 3) \times \frac{2}{(2 x - 1) - (\ln | 2 x - 1 |)}}{{(x + 3)}^{2}}

\frac{d y}{d x} = \frac{\frac{2 (x + 3)}{(2 x - 1)} - (\ln | 2 x - 1 |)}{{(x + 3)}^{2}}

\frac{d y}{d x} = \frac{2}{(x + 3) (2 x - 1)} - \frac{(\ln | 2 x - 1 |)}{{(x + 3)}^{2}}

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