# Step-by-step Solution

## Derive the function $arcsin\left(\frac{}{4}\sin\left(x\right)\right)$ with respect to x

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

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

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(arcsin\left(\sin\left(x\right)\cdot\frac{}{4}\right)\right)$
1

Taking the derivative of arcsine

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

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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

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

### Main topic:

Differential calculus

~ 0.94 seconds

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!