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mattgondek4

Answered question

2021-11-09

Find the derivatives of the function.

y = \frac{5 x - 7}{2 x + 1}

The derivative is y'=

Answer & Explanation

Theodore Schwartz

Skilled2021-11-10Added 99 answers

Step 1
Consider the function;

y = \frac{5 x - 7}{2 x + 1}

Step 2
Apply the quotient rules of derivatives,
Differentiating with respect to “x”

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

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

= \frac{(2 x + 1) (5 \cdot 1 - 0) - (5 x - 7) (2 \cdot 1 + 0)}{{(2 x + 1)}^{2}}

= \frac{10 x + 5 - (10 x - 14)}{{(2 x + 1)}^{2}}

= \frac{10 x + 5 - 10 x + 14}{{(2 x + 1)}^{2}}

y^{'} = \frac{19}{{(2 x + 1)}^{2}}

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