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Find the derivative of $\frac{1}{2}\tan\left(x\right)\sin\left(2x\right)$

Used Formulas

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Solution

Formulas

Videos

Basic Derivatives

$\frac{d}{dx}\left(\frac{x}{c}\right)=\frac{1}{c}\frac{d}{dx}\left(x\right)$
· Product rule for derivatives
$\frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Derivatives of trigonometric functions

· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right)$
· Derivative of tangent function
$\frac{d}{dx}\left(\tan\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\sec\left(\theta \right)^2$

Function Plot

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

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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:

Similar Problems Solved

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

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

$\frac{d}{dx}\sin\left(8x\right)$

$\frac{d}{dx}\left(x^3e^x\right)$

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 (6)

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