Answered: "Derivatives Find and simplify the derivative of the..."

Jason Farmer

Answered question

2021-10-12

Derivatives Find and simplify the derivative of the following functions

g (x) = \frac{x^{\frac{4}{3}} - 1}{x^{\frac{4}{3}} + 1}

2k1enyvp

Skilled2021-10-13Added 94 answers

Step 1
To find the derivative of the function,

g (x) = \frac{x^{\frac{4}{3}} - 1}{x^{\frac{4}{3}} + 1}

Step 2
The derivative of the function g(x) is given by,

g^{'} (x) = \frac{(x^{\frac{4}{3}} + 1) \frac{d (x^{\frac{4}{3}} - 1)}{d x} - (x^{\frac{4}{3}} - 1) \frac{d (x^{\frac{4}{3}} + 1)}{d x}}{{(x^{\frac{4}{3}} + 1)}^{2}}

= \frac{(x^{\frac{4}{3}} + 1) \frac{4}{3} x^{\frac{1}{3}} - (x^{\frac{4}{3}} - 1) \frac{4}{3} x^{\frac{1}{3}}}{{(x^{\frac{4}{3}} + 1)}^{2}}

= \frac{r (x + x^{\frac{1}{3}} - x + x^{\frac{1}{3}})}{3 {(x^{\frac{4}{3}} + 1)}^{2}}

= \frac{8 x^{\frac{1}{3}}}{3 {(x^{\frac{4}{3}} + 1)}^{2}}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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