$\frac{d}{dx}\left(\mathrm{tanh}\left(\frac{y}{x}\right)\right)$

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Final answer to the problem

$\frac{-y\mathrm{sech}\left(\frac{y}{x}\right)^2}{x^2}$
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Step-by-step Solution

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Apply the trigonometric identity: $\frac{d}{dx}\left(\mathrm{tanh}\left(\theta \right)\right)$$=\mathrm{sech}\left(\theta \right)^2\frac{d}{dx}\left(\theta \right)$, where $x=\frac{y}{x}$

$\mathrm{sech}\left(\frac{y}{x}\right)^2\frac{d}{dx}\left(\frac{y}{x}\right)$

Learn how to solve calcolo differenziale problems step by step online.

$\mathrm{sech}\left(\frac{y}{x}\right)^2\frac{d}{dx}\left(\frac{y}{x}\right)$

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Learn how to solve calcolo differenziale problems step by step online. d/dx(tanh(y/x)). Apply the trigonometric identity: \frac{d}{dx}\left(\mathrm{tanh}\left(\theta \right)\right)=\mathrm{sech}\left(\theta \right)^2\frac{d}{dx}\left(\theta \right), where x=\frac{y}{x}. Apply the formula: \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}, where a=y and b=x. Apply the formula: \frac{d}{dx}\left(c\right)=0, where c=y. Apply the formula: x+0=x, where x=-y\frac{d}{dx}\left(x\right).

Final answer to the problem

$\frac{-y\mathrm{sech}\left(\frac{y}{x}\right)^2}{x^2}$

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Plotting: $\frac{-y\mathrm{sech}\left(\frac{y}{x}\right)^2}{x^2}$

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1
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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

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