Derivative of Arctan Function | Simple Calc Problem

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In summary, arctan, or arctangent, is an inverse trigonometric function used to find the angle of a right triangle. It is calculated by taking the ratio of the opposite and adjacent sides in a right triangle. The range of arctan is from -π/2 to π/2, and it is used in fields such as engineering, physics, and astronomy to calculate angles and slopes. Arctan is the inverse function of tan, which is used to find the ratio of sides in a right triangle.
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ApeXX
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Homework Statement



Find the derivative of the function. Simplify if possible.

y = arctan (x + sqrt(1+x^2))

Homework Equations



I know there's something like... y = arctan(x) = ( x = tan(y) )

I'm not sure how to manipulate it...

The Attempt at a Solution



I'm not really sure how to start, any help would be greatly appreciated.

Thanks!
 
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  • #2
You probably know the derivative of arctan. If so, just differentiate it using the chain rule and do some algebra to simplify it.
 

FAQ: Derivative of Arctan Function | Simple Calc Problem

What is arctan?

Arctan, or arctangent, is an inverse trigonometric function that is used to find the angle of a right triangle given the ratio of its sides.

How is arctan calculated?

Arctan is calculated by taking the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle.

What is the range of arctan?

The range of arctan is from -π/2 to π/2, or -90 degrees to 90 degrees.

How is arctan used in real life?

Arctan is used in real life to calculate angles in fields such as engineering, physics, and astronomy. It can also be used to find the slope of a line in mathematics.

What is the difference between arctan and tan?

Arctan and tan are inverse functions of each other. While tan is used to find the ratio of sides in a right triangle, arctan is used to find the angle given the ratio of sides.

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