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Find the derivative $\frac{d}{dx}\left(\frac{3\left(1-\sin\left(x\right)\right)}{2\cos\left(x\right)}\right)$

Step-by-step Solution

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Final Answer

$\frac{-3+3\sin\left(x\right)}{2\cos\left(x\right)^2}$
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Step-by-step Solution

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Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{2\frac{d}{dx}\left(3\left(1-\sin\left(x\right)\right)\right)\cos\left(x\right)-3\frac{d}{dx}\left(2\cos\left(x\right)\right)\left(1-\sin\left(x\right)\right)}{\left(2\cos\left(x\right)\right)^2}$

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

$\frac{2\frac{d}{dx}\left(3\left(1-\sin\left(x\right)\right)\right)\cos\left(x\right)-3\frac{d}{dx}\left(2\cos\left(x\right)\right)\left(1-\sin\left(x\right)\right)}{\left(2\cos\left(x\right)\right)^2}$

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Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((3(1-sin(x)))/(2cos(x))). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant (3) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function.

Final Answer

$\frac{-3+3\sin\left(x\right)}{2\cos\left(x\right)^2}$

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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 3(1+-1sinx)/2cosx using the product ruleFind derivative of 3(1+-1sinx)/2cosx using the quotient ruleFind derivative of 3(1+-1sinx)/2cosx using logarithmic differentiation

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

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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: Quotient Rule of Differentiation

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

Used Formulas

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