Question

Differentiate ax wrt x from first principles.

Solution

Correct option is

f’(x) = ax log a.

 

Let f (x) = ax

Using the definition of derivatives,

          

                   

Hence f’(x) = ax log a.

SIMILAR QUESTIONS

Q1

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q2

Let f is a differentiable function such that   

     .

Q3

Let f be a function such that  .   

.

Q4

Find and b so that the function:    

 

   

Q5

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

Q6

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.

 

Q7

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

Q8

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

Q9

Find the derivative of sin x wrt x from first principles.

Q10

Differentiate sin (log x) wrt x from first principles.