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Find the derivative of $\arctan\left(x\right)\mathrm{arccot}\left(x\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{\mathrm{arccot}\left(x\right)-\arctan\left(x\right)}{1+x^2}$
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Step-by-step Solution

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative of arctan(x)arccot(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\arctan\left(x\right) and g=\mathrm{arccot}\left(x\right). Taking the derivative of arctangent. The derivative of the linear function is equal to 1. Multiply the fraction by the term .

Final answer to the problem

$\frac{\mathrm{arccot}\left(x\right)-\arctan\left(x\right)}{1+x^2}$

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Function Plot

Plotting: $\frac{\mathrm{arccot}\left(x\right)-\arctan\left(x\right)}{1+x^2}$

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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:

Similar Problems Solved

$\frac{d}{dx}\left(x\arctan\left(x\right)\right)$

$\frac{d}{dx}\left(\arcsin\left(x^3\right)\right)$

$\frac{d}{dx}\arcsin\left(\sqrt{x}\right)$

$\frac{d}{dx}\left(\arcsin\left(\sqrt{2x}\right)\right)$

$\frac{d}{dx}\left(\arccot\left(\sqrt{x}\right)\right)$

$\frac{d}{dx}\left(\arcsin\sqrt{x}\right)$

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

Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

See formulas (4)

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