"Derivatives Find and simplify the derivative of the..." solved and explained

illusiia

Answered question

2021-10-05

Derivatives Find and simplify the derivative of the following functions

p (x) = \frac{4 x^{3} + 3 x + 1}{2 x^{5}}

Daphne Broadhurst

Skilled2021-10-06Added 109 answers

Step 1
Given:

p (x) = \frac{4 x^{3} + 3 x + 1}{2 x^{5}}

for finding derivative of given function, first we simplify given expression then find derivative of it
Step 2
so,

p (x) = \frac{4 x^{3} + 3 x + 1}{2 x^{5}}

= \frac{4 x^{3}}{2 x^{5}} + \frac{2 x}{2 x^{5}} + \frac{1}{2 x^{5}}

= 2 x^{- 2} + x^{- 4} + \frac{x^{- 5}}{2}

now differentiating it
so,

\frac{d}{d x} [p (x)] = \frac{d}{d x} [2 x^{- 2} + x^{- 4} + \frac{x^{- 5}}{2}]

= 2 \frac{d}{d x} (x^{- 2}) + \frac{d}{d x} (x^{- 4}) + \frac{1}{2} \frac{d}{d x} (x^{- 5})

(∵ \frac{d}{d x} (x^{n}) = n x^{n - 1})

= 2 (- 2 x^{- 3}) + (- 4 x^{- 5}) + \frac{1}{2} (- 5 x^{- 6})

= - \frac{4}{x^{3}} - \frac{4}{x^{5}} - \frac{5}{2 x^{6}}

= - \frac{8 x^{3} + 8 x + 5}{2 x^{6}}

Step 3
hence, derivative of given function is

- \frac{8 x^{3} + 8 x + 5}{2 x^{6}}

Jeffrey Jordon

Expert2022-08-13Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?