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Find the derivative of $\frac{x^3+x-1}{x^4+6x^2+9}$ using the definition

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 Solution

 Videos

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Calculus - How find the first derivative using a chart, 1/f(x) at x=1

https://www.youtube.com/watch?v=V5OROgIBnDc

Calculus - Learn how to take derivative using quotient rule by simplifying first, f(x)=x(1- 4/(x+3))

https://www.youtube.com/watch?v=Mqjiw5Ax_4w

Calculus - Use quotient rule to take derivative with trigonometric functions, y=(1-cosx)/sinx

https://www.youtube.com/watch?v=BAa7KHPk7bA

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

https://www.youtube.com/watch?v=urYZhqwUTI0

Finding the derivative square root x over x, using power rule

https://www.youtube.com/watch?v=oR6DDJ-rvbQ

 Function Plot

Plotting: $\frac{3x^2+1}{y^2+6y+9}$

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1

2

3

4

5

6

7

8

9

0



a

b

c

d

f

g

m

n

u

v

w

x

y

z

.

(◻)

+

-

×

◻/◻

/

÷

◻²

◻^◻

√◻

√

^◻√◻

^◻√

∞

e

π

ln

log

log_◻

lim

d/dx

D^□_x

∫

∫^◻

|◻|

θ

=

>

<

>=

<=

sin

cos

tan

cot

sec

csc

asin

acos

atan

acot

asec

acsc

sinh

cosh

tanh

coth

sech

csch

asinh

acosh

atanh

acoth

asech

acsch

 How to improve your answer:

 Main Topic: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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