`y = (tan^-1(x^2))` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 50 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = tan^(-1)x ; then dy/dx = 1/{1+(x^2)}

2) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number

Clearly, the given function contains sub-functions, so the chain rule of differentiation will be followed

Hence,

y = tan^(-1)(x^2)` `

dy/dx = y' = [1/{1 + (x^4)}]*(2x)

or, dy/dx = 2x/{1 + (x^4)}

` `

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