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# Find the derivative $\frac{d}{dx}\left(\frac{5\sin\left(2\right)\tan\left(2x\right)^5}{\cos\left(2\right)}\right)$

## Step-by-step Solution

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###  Videos

$-109.251899\tan\left(2x\right)^{4}\sec\left(2x\right)^2$
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##  Step-by-step Solution 

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(\frac{4.546485\tan\left(2x\right)^5}{-\frac{67}{161}}\right)$

Learn how to solve quotient rule of differentiation problems step by step online.

$\frac{d}{dx}\left(\frac{4.546485\tan\left(2x\right)^5}{-\frac{67}{161}}\right)$

Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((5tan(2x)^5sin(2))/cos(2)). Simplify the derivative by applying the properties of logarithms. Take \frac{4.546485}{-\frac{67}{161}} out of the fraction. The derivative of a function multiplied by a constant (-10.92519) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

$-109.251899\tan\left(2x\right)^{4}\sec\left(2x\right)^2$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of 5tan2x^5/cos2 using the product ruleFind derivative of 5tan2x^5/cos2 using the quotient ruleFind derivative of 5tan2x^5/cos2 using logarithmic differentiation

SnapXam A2

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5
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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
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

### Main Topic: Quotient Rule of Differentiation

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

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