If for x ∈ 0 , 1 4 , the derivative of tan - 1 ⁡ 6 x x 1 - 9 x 3 is x ⋅ g x , then g x equals:

Question

If for x ∈ 0 , 1 4 , the derivative of tan - 1 ⁡ 6 x x 1 - 9 x 3 is x ⋅ g x , then g x equals:, 9 1 + 9 x 3, 3 x x 1 - 9 x 3, 3 x 1 - 9 x 3, 3 1 + 9 x 3

MARKS App · Accepted Answer

Let 3 x 3 2 = y , then y ∈ 0 , 3 8 tan - 1 ⁡ 6 x x 1 - 9 x 3 = tan - 1 ⁡ 2 y 1 - y 2 ⇒ 2 tan - 1 ⁡ y = 2 tan - 1 ⁡ 3 x 3 2 Now ⇒ d d x 2 tan - 1 ⁡ 3 x 3 2 = 2 1 + 9 x 3 ⋅ 3 ⋅ 3 2 ⋅ x 1 2 ⇒ d d x 2 tan - 1 ⁡ 3 x 3 2 = 9 1 + 9 x 3 ⋅ x ⇒ x . g x = 9 1 + 9 x 3 ⋅ x ⇒ g x = 9 1 + 9 x 3

Search any question & find its solution

Looking for more such questions to practice?