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

Step-by-step Solution

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Final answer to the problem

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

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Apply the formula: $derivdef\left(x\right)$$=\lim_{h\to0}\left(\frac{eval\left(x,var+h\right)-x}{h}\right)$, where $derivdefx=derivdef\left(\sin\left(2x\right)\right)$ and $x=\sin\left(2x\right)$

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

Learn how to solve definizione di derivato problems step by step online.

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

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Learn how to solve definizione di derivato problems step by step online. d/dx(sin(2x)). Apply the formula: derivdef\left(x\right)=\lim_{h\to0}\left(\frac{eval\left(x,var+h\right)-x}{h}\right), where derivdefx=derivdef\left(\sin\left(2x\right)\right) and x=\sin\left(2x\right). Multiply the single term 2 by each term of the polynomial \left(x+h\right). Apply the trigonometric identity: \sin\left(x+y\right)=\sin\left(x\right)\cos\left(y\right)+\cos\left(x\right)\sin\left(y\right), where x+y=2x+2h, x=2x and y=2h. Apply the formula: ax+bx=x\left(a+b\right), where a=\cos\left(2h\right), b=-1 and x=\sin\left(2x\right).

Final answer to the problem

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

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

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0
a
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g
m
n
u
v
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x
y
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.
(◻)
+
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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

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