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 x/((x^2+y^2)^0.5)

### Formulas

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

## Step-by-step explanation

Problem

$\frac{d}{dx}\left(\frac{x}{\sqrt{x^2+y^2}}\right)$
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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

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

### Struggling with math?

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

$\frac{d}{dx}\left(\frac{x}{\sqrt{x^2+y^2}}\right)$

### Main topic:

Differential calculus

0.34 seconds