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Find the derivative of $\cos\left(x\right)\csc\left(x\right)$

Step-by-step Solution

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Final Answer

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

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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\cos\left(x\right)$ and $g=\csc\left(x\right)$

$\frac{d}{dx}\left(\cos\left(x\right)\right)\csc\left(x\right)+\cos\left(x\right)\frac{d}{dx}\left(\csc\left(x\right)\right)$

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$\frac{d}{dx}\left(\cos\left(x\right)\right)\csc\left(x\right)+\cos\left(x\right)\frac{d}{dx}\left(\csc\left(x\right)\right)$

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Learn how to solve factor problems step by step online. Find the derivative of cos(x)csc(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=\csc\left(x\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Applying the trigonometric identity: \sin\left(\theta\right)\cdot\csc\left(\theta\right)=1. Taking the derivative of cosecant function: \frac{d}{dx}\left(\csc(x)\right)=-\csc(x)\cdot\cot(x)\cdot D_x(x).

Final Answer

$-\csc\left(x\right)^2$

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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 cosxcscx using the product ruleFind derivative of cosxcscx using the quotient ruleFind derivative of cosxcscx using logarithmic differentiation

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1
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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
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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Main Topic: Factor

Factor the expression.

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