Is Cot-1x the Same as 1/Tan-1x?

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In summary, the derivative of inverse Cotangent is equal to 1/(1+x^2) or 1/(1+cot^-1(x)^2), derived using the chain rule. It cannot be simplified further and has a domain of all real numbers except -1 and 1, and a range of all real numbers. In real life, it is used in various fields such as physics, engineering, and economics for finding rates of change and solving real-world problems. It is also used in calculating integrals and studying trigonometric functions.
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Jules18
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My notes say the deriv. of inverse Cotangent is -1/(1+x2)

But when I plot the derivative of this function: 1/Tan-1x
against -1/(1+x2), I get two different graphs.

Is Cot-1x not the same thing as 1/Tan-1x ?

~Jules~
 
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  • #2


They are not the same.

Let y = cot-1x
cot y = x
1/coty = tan y = 1/x
y = tan-1(1/x)

cot-1x = tan-1(1/x)
 
  • #3


thanks
 

FAQ: Is Cot-1x the Same as 1/Tan-1x?

What is the derivative of inverse Cotangent?

The derivative of inverse Cotangent is equal to 1/(1+x^2). This can also be written as 1/(1+cot^-1(x)^2).

How is the derivative of inverse Cotangent derived?

The derivative of inverse Cotangent can be derived using the chain rule. First, we rewrite cot^-1(x) as arccot(x). Then, we use the identity cot(arccot(x)) = x to simplify the expression. Finally, we apply the chain rule to find the derivative.

Can the derivative of inverse Cotangent be simplified further?

No, the derivative of inverse Cotangent cannot be simplified any further. It is already in its simplest form of 1/(1+x^2) or 1/(1+cot^-1(x)^2).

What is the domain and range of the derivative of inverse Cotangent?

The domain of the derivative of inverse Cotangent is all real numbers except for -1 and 1. The range is all real numbers.

How is the derivative of inverse Cotangent used in real life?

The derivative of inverse Cotangent is used in many fields, including physics, engineering, and economics. It is used to find rates of change and slopes of curves, which can help in optimizing processes and solving real-world problems. It is also used in calculating integrals and in the study of trigonometric functions.

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