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Algebra Baldor
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Find the derivative $\frac{d}{dx}\left(\frac{x^2\left(x-6\right)^9}{\left(x^2+6\right)^4}\right)$

Used Formulas

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Solution

Formulas

Videos

Basic Derivatives

· Derivative of the natural logarithm
$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$

Function Plot

Plotting: $\left(\frac{2}{x}+\frac{9}{x-6}+\frac{-8x}{x^2+6}\right)\frac{x^2\left(x-6\right)^9}{\left(x^2+6\right)^4}$

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0
a
b
c
d
f
g
m
n
u
v
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x
y
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(◻)
+
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×
◻/◻
/
÷
◻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:

Similar Problems Solved

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$\frac{d}{dx}\left(\frac{2x^3}{\left(2-5x\right)\sqrt{x^2+1}}\right)$

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$\frac{d}{dx}\ln\left(x^2+1\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{\left(x^5+3x\right)^4}{cos\:x}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{3}{x^2}\right)$

Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.

Used Formulas

See formulas (6)

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