Math virtual assistant

About Snapxam Calculators Topics Go Premium
Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

Find the derivative of ln(arccos(1/(x^0.5)))

Answer

$\frac{\frac{1}{2}}{\sqrt{x^{3}}\sqrt{\frac{-1}{x}+1}arccos\left(\frac{1}{\sqrt{x}}\right)}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\ln\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\right)$
1

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{d}{dx}\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\frac{1}{arccos\left(\frac{1}{\sqrt{x}}\right)}$

Answer

$\frac{\frac{1}{2}}{\sqrt{x^{3}}\sqrt{\frac{-1}{x}+1}arccos\left(\frac{1}{\sqrt{x}}\right)}$

Struggling with math?

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

$\frac{d}{dx}\left(\ln\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\right)$

Main topic:

Differential calculus

~ 0.77 seconds