Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Derive the function $arcsin\left(\cos\left(\frac{x}{3}\right)\right)$ with respect to x

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
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

Answer

$-0.3333$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(arcsin\left(\cos\left(\frac{x}{3}\right)\right)\right)$
1

Taking the derivative of arcsine

$\frac{1}{\sqrt{1-\cos\left(\frac{x}{3}\right)^2}}\cdot\frac{d}{dx}\left(\cos\left(\frac{x}{3}\right)\right)$
2

The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if $f(x) = \cos(x)$, then $f'(x) = -\sin(x)\cdot D_x(x)$

$-\frac{1}{\sqrt{1-\cos\left(\frac{x}{3}\right)^2}}\sin\left(\frac{x}{3}\right)\frac{d}{dx}\left(\frac{x}{3}\right)$

Unlock this step-by-step solution!

Answer

$-0.3333$
$\frac{d}{dx}\left(arcsin\left(\cos\left(\frac{x}{3}\right)\right)\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.89 seconds