# Step-by-step Solution

## Find the derivative of $\frac{1}{2}\left(x\sqrt{4-x^2}+4arcsin\left(\frac{x}{2}\right)\right)$

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

$\frac{1}{2}\sqrt{4-x^2}-\frac{1}{2}\left(4-x^2\right)^{-\frac{1}{2}}x^2+\frac{1}{2}\left(\frac{2}{\sqrt{1+\frac{-x^2}{4}}}\right)$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{1}{2}\cdot \left(x\sqrt{4-x^2}+4arcsin\left(\frac{x}{2}\right)\right)\right)$
1

Solve the product $\frac{1}{2}\left(x\sqrt{4-x^2}+4arcsin\left(\frac{x}{2}\right)\right)$

$\frac{d}{dx}\left(\frac{1}{2}x\sqrt{4-x^2}+2arcsin\left(\frac{x}{2}\right)\right)$
2

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(\frac{1}{2}x\sqrt{4-x^2}\right)+\frac{d}{dx}\left(2arcsin\left(\frac{x}{2}\right)\right)$

$\frac{1}{2}\sqrt{4-x^2}-\frac{1}{2}\left(4-x^2\right)^{-\frac{1}{2}}x^2+\frac{1}{2}\left(\frac{2}{\sqrt{1+\frac{-x^2}{4}}}\right)$
$\frac{d}{dx}\left(\frac{1}{2}\cdot \left(x\sqrt{4-x^2}+4arcsin\left(\frac{x}{2}\right)\right)\right)$

### Main topic:

Differential calculus

~ 0.82 seconds