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Find the derivative of $\arctan\left(\frac{x}{y}\right)$

Step-by-step Solution

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Final Answer

$\frac{y}{x^2+y^2}$
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Step-by-step Solution

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Taking the derivative of arctangent

$\frac{1}{1+\left(\frac{x}{y}\right)^2}\frac{d}{dx}\left(\frac{x}{y}\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{1}{1+\left(\frac{x}{y}\right)^2}\frac{d}{dx}\left(\frac{x}{y}\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of arctan(x/y). Taking the derivative of arctangent. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Combine 1+\frac{x^2}{y^2} in a single fraction. Divide fractions \frac{1}{\frac{x^2+y^2}{y^2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

Final Answer

$\frac{y}{x^2+y^2}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of arctan(x/y) using the product ruleFind derivative of arctan(x/y) using the quotient ruleFind derivative of arctan(x/y) using logarithmic differentiationFind derivative of arctan(x/y) using the definition

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Function Plot

Plotting: $\frac{y}{x^2+y^2}$

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1
2
3
4
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
Dx
|◻|
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:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

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