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Find the implicit derivative $\frac{d}{dx}\left(y=\arctan\left(\frac{x}{y}\right)\right)$

Used Formulas

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Solution

Formulas

Videos

Basic Differentiation Rules

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Quotient Rule in Differentiation
$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$

Derivatives of inverse trigonometric functions

$\frac{d}{dx}\left(\arctan\left(\theta \right)\right)=\frac{1}{1+\theta ^2}\frac{d}{dx}\left(\theta \right)$

Function Plot

Plotting: $y^{\prime}=\frac{y-xy^{\prime}}{x^2+y^2}$

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main Topic: Inverse trigonometric functions differentiation

Describes how to find the derivative of the inverse of the trigonometric functions sine, cosine, tangent, etc.

Used Formulas

See formulas (3)

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