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Find the derivative of $\frac{\tan\left(t\right)+\cot\left(t\right)}{\cot\left(t\right)}$

Step-by-step Solution

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Final Answer

$\frac{\sec\left(t\right)^2\cot\left(t\right)+\tan\left(t\right)\csc\left(t\right)^2}{\cot\left(t\right)^2}$
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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{\frac{d}{dt}\left(\tan\left(t\right)+\cot\left(t\right)\right)\cot\left(t\right)-\left(\tan\left(t\right)+\cot\left(t\right)\right)\frac{d}{dt}\left(\cot\left(t\right)\right)}{\cot\left(t\right)^2}$

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$\frac{\frac{d}{dt}\left(\tan\left(t\right)+\cot\left(t\right)\right)\cot\left(t\right)-\left(\tan\left(t\right)+\cot\left(t\right)\right)\frac{d}{dt}\left(\cot\left(t\right)\right)}{\cot\left(t\right)^2}$

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Learn how to solve problems step by step online. Find the derivative of (tan(t)+cot(t))/cot(t). 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}}. Simplify the product -(\tan\left(t\right)+\cot\left(t\right)). Taking the derivative of cotangent. Simplify the product -(-\tan\left(t\right)-\cot\left(t\right)).

Final Answer

$\frac{\sec\left(t\right)^2\cot\left(t\right)+\tan\left(t\right)\csc\left(t\right)^2}{\cot\left(t\right)^2}$

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 derivative of (tant+cott)/cott using the product ruleFind derivative of (tant+cott)/cott using the quotient ruleFind derivative of (tant+cott)/cott using logarithmic differentiation

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Function Plot

Plotting: $\frac{\sec\left(t\right)^2\cot\left(t\right)+\tan\left(t\right)\csc\left(t\right)^2}{\cot\left(t\right)^2}$

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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

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