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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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Final answer to the problem

$-109.2519995\tan\left(2x\right)^{4}\sec\left(2x\right)^2$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(-10.9252\tan\left(2x\right)^5\right)$

Learn how to solve integrals of polynomial functions problems step by step online.

$\frac{d}{dx}\left(-10.9252\tan\left(2x\right)^5\right)$

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Learn how to solve integrals of polynomial functions 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. The derivative of a function multiplied by a constant 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}. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}.

Final answer to the problem

$-109.2519995\tan\left(2x\right)^{4}\sec\left(2x\right)^2$

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Function Plot

Plotting: $-109.2519995\tan\left(2x\right)^{4}\sec\left(2x\right)^2$

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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

How to improve your answer:

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

See formulas (1)

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