illusiia

2021-10-05

Derivatives Find and simplify the derivative of the following functions

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

Daphne Broadhurst

Skilled2021-10-06Added 109 answers

Step 1

Given:$p\left(x\right)=\frac{4{x}^{3}+3x+1}{2{x}^{5}}$

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

Step 2

so,

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

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

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

now differentiating it

so,

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

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

$(\because \frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1})$

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

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

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

Step 3

hence, derivative of given function is$-\frac{8{x}^{3}+8x+5}{2{x}^{6}}$ .

Given:

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

Step 2

so,

now differentiating it

so,

Step 3

hence, derivative of given function is

Jeffrey Jordon

Expert2022-08-13Added 2605 answers

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?

How do I find the y-intercept of a parabola?

What are the vertices of $9{x}^{2}+16{y}^{2}=144$?

How to determine the rate of change of a function?

Why are the tangents for 90 and 270 degrees undefined?

How to find the center and radius of the circle ${x}^{2}+{y}^{2}-6x+8y=0$?

What is multiplicative inverse of a number?

How to find the continuity of a function on a closed interval?

How do I find the tangent line of a function?

How to find vertical asymptotes using limits?

How to find the center and radius of the circle ${x}^{2}-12x+{y}^{2}+4y+15=0$?

Let f be a function so that (below). Which must be true?

I. f is continuous at x=2

II. f is differentiable at x=2

III. The derivative of f is continuous at x=2

(A) I (B) II (C) I and II (D) I and III (E) II and IIIHow to find the center and radius of the circle given ${x}^{2}+{y}^{2}+8x-6y=0$?

How to find the center and radius of the circle ${x}^{2}+{y}^{2}+4x-8y+4=0$?

How to identify the center and radius of the circle ${(x+3)}^{2}+{(y-8)}^{2}=16$?