Find the derivative of e^(tan-1(x))

Question

asked Dec 21, 2017 51.7k views

1 Answer

Billmalarky · Answer 1 · 2017-12-26T02:26:48+0000

Answer:

$\displaystyle (dy)/(dx) = (e^(\arctan x))/(x^2 + 1)$

General Formulas and Concepts:

Calculus

Differentiation

Derivative Rule [Chain Rule]:
$\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)$

Explanation:

Step 1: Define

Identify

$\displaystyle y = e^(\arctan x)$

Step 2: Differentiate

Exponential Differentiation [Derivative Rule - Chain Rule]:
$\displaystyle y' = e^(\arctan x)(\arctan x)'$
Trigonometric Differentiation:
$\displaystyle y' = (e^(\arctan x))/(x^2 + 1)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation