We have an answer to "Find the derivatives of the functions y=(1+x2)etan−1x"

College
Calculus and Analysis
Differential Calculus
Derivatives

grasaladae5

Answered question

2021-12-07

Find the derivatives of the functions

y = (1 + x^{2}) e^{\tan^{- 1} x}

Answer & Explanation

Keith Dooley

Beginner2021-12-08Added 14 answers

Step 1
Given,
$y = (1 + x^{2}) e^{\tan^{- 1} x}$
Step 2
differentiate w.r.t "x"
$\frac{d y}{d x} = (2 x) e^{\tan^{- 1} x} + (1 + x^{2}) e^{\tan^{- 1} x} (\frac{1}{1 + x^{2}})$
$\frac{d y}{d x} = 2 x e^{\tan^{- 1} x} + e^{\tan^{- 1} x}$
$\frac{d y}{d x} = (2 x + 1) e^{\tan^{- 1} x}$

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