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

Step-by-step Solution

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Solution

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Final Answer

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

Problem to solve:

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

Specify the solving method

1

The derivative of a function multiplied by a constant ($2$) is equal to the constant times the derivative of the function

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

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

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

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Unlock the first 2 steps of this solution.

Learn how to solve differential calculus problems step by step online. Find the derivative of 2sin(x/2). The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(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.

Final Answer

$\cos\left(\frac{x}{2}\right)$

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(2sin(x/2)) using the product ruleFind d/dx(2sin(x/2)) using the quotient ruleFind d/dx(2sin(x/2)) using logarithmic differentiationFind d/dx(2sin(x/2)) using the definition

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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
D□x
∫
∫◻
|◻|
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:

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$\frac{d}{dx}\left(2x+1\right)$

Main topic:

Differential Calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.05 s

Related topics:

Differential CalculusCalculusBasic Differentiation Rules

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