Differentiate tan^-1 (√(1+x^2)-1)/(x) w.r.t. tan^-1 x |...

Name: Problem 206, Chapter 4: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2022-02-21T17:25:01-08:00
Duration: 6 min 48 s
Channel: M Hassan Anwar
Description: Differentiate tan^-1 (√(1+x^2)-1)/(x) w.r.t. tan^-1 x

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as the arctan function, have specific derivative formulas that are essential in calculus. For example, the derivative of arctan(x) is 1/(1+x²). Understanding these derivatives is key when these functions appear as parts of more complex expressions.

Differentiation of Radical Functions

Differentiating radical functions involves rewriting the radical expression in exponent form and then applying the chain rule along with the power rule. This technique is essential when encountering square roots, as it helps in simplifying and accurately computing the derivative of expressions that include radicals.

Quotient Rule

The quotient rule is used to differentiate functions that are expressed as the ratio of two differentiable functions. It provides a way to correctly account for the change in both the numerator and denominator by taking their derivatives and combining them appropriately in the formula (u'v - uv')/v².

Chain Rule

The chain rule is a fundamental differentiation technique used when dealing with composite functions. It allows you to differentiate a function composed of other functions by multiplying the derivative of the outer function, evaluated at the inner function, by the derivative of the inner function. This concept is crucial when the variable of interest is a function of another variable.

Differentiation with Respect to Another Function

When you are asked to differentiate one function with respect to another function, you use the idea of the derivative as a ratio of differentials. This is done by computing the derivative of the numerator function with respect to x and dividing it by the derivative of the denominator function with respect to x. This method is especially important when the variable of differentiation is itself a function of x.

Transcript

Please give Ace some feedback