Question

Find the derivative of y = log x wrt x from first principles.

Solution

Correct option is

1/x

Let f (x) = log x

Using definition of derivative,

          

                     

                     

                     

SIMILAR QUESTIONS

Q1

Let f : → R, such that f’ (0) = 1 and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy∀ xy Ïµ R. Find f (x).

Q2

If g(x) is continuous function in [0, ∞) satisfying g(1) = 1. If

                          .

Q3

Let f is a differentiable function such that 

          .

Q4

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q5

Let f is a differentiable function such that   

     .

Q6

Let f be a function such that  .   

.

Q7

Find and b so that the function:    

 

   

Q8

 is continuous at x = 0, find the values of Aand B. Also find f (0).

Q9

Find the natural number a for which  where the function f satisfies the relation f (x + y) = f (xf (y) for all natural number xy and further f (1) = 2.

 

Q10

Evaluate the derivative of f (x) = xn wrt x from definition of derivative. Hence find the derivative of wrt x.