Step-by-step Solution

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

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sinh
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asinh
acosh
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Step-by-step Solution

Problem to solve:

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

Solving method

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

$\lim_{h\to0}\left(\frac{\sin\left(2\left(x+h\right)\right)-\sin\left(2x\right)}{h}\right)$

Unlock this full step-by-step solution!

Learn how to solve differential calculus problems step by step online. Find the derivative of sin(2x). Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \sin\left(2x\right). Substituting f(x+h) and f(x) on the limit. Solve the product 2\left(x+h\right). Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals 2x, and angle \beta equals 2h. Factoring by \sin\left(2x\right).

Final Answer

$2\cos\left(2x\right)$
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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

Tips on how to improve your answer:

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

Main topic:

Differential Calculus

Related Formulas:

1. See formulas

Time to solve it:

~ 0.67 s