NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

The rate of change of ( x 2 + 16 ) with respect to x x - 1 at x = 3 is

Options

A2
B11 5
C- 12 5
D- 3

Correct answer

C. - 12 5

Step-by-step solution

Let y = x 2 + 16   a n d   z = x x - 1 On differentiating w.r.t., x , we get, d z d x = x - 1 - x x - 1 2 = - 1 x - 1 2 and d y d x = 1 × 2 x 2 x 2 + 16 ⇒ d y d z = x x 2 + 16   - 1 x - 1 2   At x = 3 d y d z = 3 5   ( 4 ) ( - 1 ) = - 12 5

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