Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
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

\frac{d}{dx}\left(\frac{3}{\ln\left(\sqrt{\sin\left(x\right)-\cos\left(x\right)}\right)}\right)

Derive the function 3/(ln((sin(x)-1cos(x))^0.5)) with respect to x

Answer

$\frac{-\frac{3}{2}\sin\left(x\right)-\frac{3}{2}\cos\left(x\right)}{\frac{1}{4}\ln\left(\sin\left(x\right)-\cos\left(x\right)\right)^2\sin\left(x\right)-\frac{1}{4}\ln\left(\sin\left(x\right)-\cos\left(x\right)\right)^2\cos\left(x\right)}$

Step-by-step explanation

Problem

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

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

Unlock this step-by-step solution!

Answer

$\frac{-\frac{3}{2}\sin\left(x\right)-\frac{3}{2}\cos\left(x\right)}{\frac{1}{4}\ln\left(\sin\left(x\right)-\cos\left(x\right)\right)^2\sin\left(x\right)-\frac{1}{4}\ln\left(\sin\left(x\right)-\cos\left(x\right)\right)^2\cos\left(x\right)}$
$\frac{d}{dx}\left(\frac{3}{\ln\left(\sqrt{\sin\left(x\right)-\cos\left(x\right)}\right)}\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.99 seconds