Get the answer to "Find the derivatives of the functions y=9x2+2x2+3" - Plainmath

OlmekinjP

Answered question

2021-10-08

Find the derivatives of the functions

y = \frac{9 x^{2} + 2}{x^{2} + 3}

Answer & Explanation

yunitsiL

Skilled2021-10-09Added 108 answers

Step 1
Given :

y = \frac{9 x^{2} + 2}{x^{2} + 3}

To find:

\frac{d}{d x} [\frac{9 x^{2} + 2}{x^{2} + 3}]

Step 2

\frac{d}{d x} [\frac{9 x^{2} + 2}{x^{2} + 3}]

= \frac{\frac{d}{d x} [9 x^{2} + 2] \cdot (x^{2} + 3) - (9 x^{2} + 2) \cdot \frac{d}{d x} [x^{2} + 3]}{{(x^{2} + 3)}^{2}}

= \frac{(9 \cdot 2 x + 0) (x^{2} + 3) - (9 x^{2} + 2) (2 x + 10)}{{(x^{2} + 3)}^{2}}

= \frac{18 x (x^{2} + 3) - 2 x (9 x^{2} + 2)}{{(x^{2} + 3)}^{2}}

= \frac{18 x}{(x^{2} + 3)} - \frac{2 x (9 x^{2} + 2)}{{(x^{2} + 3)}^{2}}

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