Find the derivative $\frac{d}{dx}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)$

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Final answer to the problem

$\sec\left(x\right)^2$
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Step-by-step Solution

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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 $a=\sin\left(x\right)$ and $b=\cos\left(x\right)$

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

Learn how to solve regola del quoziente di differenziazione problems step by step online.

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

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Learn how to solve regola del quoziente di differenziazione problems step by step online. Find the derivative d/dx(sin(x)/cos(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=\sin\left(x\right) and b=\cos\left(x\right). Apply the trigonometric identity: \frac{d}{dx}\left(\sin\left(\theta \right)\right)=\cos\left(\theta \right). Apply the formula: x\cdot x=x^2, where x=\cos\left(x\right). Apply the trigonometric identity: \frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\sin\left(\theta \right).

Final answer to the problem

$\sec\left(x\right)^2$

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Plotting: $\sec\left(x\right)^2$

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7
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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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