Find the derivative of 7 + x 2 2 + x + 7 x 2 + 7 x 3 .

Trying my answerDifferentiate using the Quotient Rule which states that&nbsp;ddx[f(x)g(x)]&nbsp;is&nbsp;g(x)ddx[f(x)]-f(x)ddx[g(x)]g(x)2&nbsp;where&nbsp;f(x)=7+x2&nbsp;and&nbsp;g(x)=2+x+7x2+7x3.(2+x+7x2+7x3)ddx[7+x2]-(7+x2)ddx[2+x+7x2+7x3](2+x+7x2+7x3)2Differentiate.2(2+x+7x2+7x3)x-(7+x2)(1+14x+21x2)(2+x+7x2+7x3)2Simplify.-7x4+146x2+94x+7(7x3+7x2+x+2)2&nbsp;

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College
Calculus and Analysis
Differential Calculus
Derivatives

mikior9t3ue

Answered question

2022-05-11

Find the derivative of

\frac{7 + x^{2}}{2 + x + 7 x^{2} + 7 x^{3}}

Answer & Explanation

Frida Wilkinson

Beginner2022-05-12Added 13 answers

Trying my answer

Differentiate using the Quotient Rule which states that $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ is $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ where $f (x) = 7 + x^{2}$ and $g (x) = 2 + x + 7 x^{2} + 7 x^{3}$ .

$\frac{(2 + x + 7 x^{2} + 7 x^{3}) \frac{d}{d x} [7 + x^{2}] - (7 + x^{2}) \frac{d}{d x} [2 + x + 7 x^{2} + 7 x^{3}]}{{(2 + x + 7 x^{2} + 7 x^{3})}^{2}}$

Differentiate.

$\frac{2 (2 + x + 7 x^{2} + 7 x^{3}) x - (7 + x^{2}) (1 + 14 x + 21 x^{2})}{{(2 + x + 7 x^{2} + 7 x^{3})}^{2}}$

Simplify.

$- \frac{7 x^{4} + 146 x^{2} + 94 x + 7}{{(7 x^{3} + 7 x^{2} + x + 2)}^{2}}$

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