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# Find the derivative $\frac{d}{dx}\left(\frac{1}{\tan\left(x\right)}\right)$

## Step-by-step Solution

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###  Videos

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

Problem to solve:

$\frac{d}{dx}\left(\frac{1}{\tan\left(x\right)}\right)$

Specify the solving method

1

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 $h(x) = \frac{f(x)}{g(x)}$, where ${g(x) \neq 0}$, then $h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}$

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

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

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

Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(1/(tan(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 derivative of the constant function (1) is equal to zero. 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)}. The derivative of the linear function is equal to 1.

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

##  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 d/dx(1/(tan(x)) using the product ruleFind d/dx(1/(tan(x)) using the quotient ruleFind d/dx(1/(tan(x)) using logarithmic differentiationFind d/dx(1/(tan(x)) using the definition

SnapXam A2

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a
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u
v
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x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

~ 0.08 s

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