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Find the derivative using the product rule $y=\frac{\sin\left(3x+x^2\right)}{\left(6-x^4\right)^3}$

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Find the derivative using quotient rule inside of the product rule

https://www.youtube.com/watch?v=7Ex6GchV4xs

Find the derivative using product rule inside quotient

https://www.youtube.com/watch?v=owgP1d_HKLs

Quotient rule and common derivatives | Taking derivatives | Differential Calculus | Khan Academy

https://www.youtube.com/watch?v=E_1gEtiGPNI

Calculus - Take the derivative using product rule with natural logarithms,, ln(y) = (x^2)ln(x)

https://www.youtube.com/watch?v=4TpfQj_Wj84

Derivatives of Composite Functions - Chain Rule, Product & Quotient Rule - Calculus Review

https://www.youtube.com/watch?v=vNXjMTv4vHs

Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=KyYC8XzKsHU

Function Plot

Plotting: $\frac{\left(3+2x\right)\left(6-x^4\right)^3\cos\left(3x+x^2\right)+12\left(6-x^4\right)^{2}x^{3}\sin\left(3x+x^2\right)}{\left(6-x^4\right)^{6}}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

See formulas (7)

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