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Find the derivative of $\tan\left(\frac{x}{2}\right)$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{2}\sec\left(\frac{x}{2}\right)^2$
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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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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 ${f'(x) = sec^2(x)\cdot D_x(x)}$

$\frac{d}{dx}\left(\frac{x}{2}\right)\sec\left(\frac{x}{2}\right)^2$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(\frac{x}{2}\right)\sec\left(\frac{x}{2}\right)^2$

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Learn how to solve differential calculus problems step by step online. Find the derivative of tan(x/2). 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 a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. Divide 1 by 2. The derivative of the linear function is equal to 1.

Final answer to the problem

$\frac{1}{2}\sec\left(\frac{x}{2}\right)^2$

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Function Plot

Plotting: $\frac{1}{2}\sec\left(\frac{x}{2}\right)^2$

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5
6
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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

See formulas (3)

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