Find the natural number a for which where the function f satisfies the relation f (x + y) = f (x) f (y) for all natural number x, y and further f (1) 2.
Find the derivative of y = log x wrt x from first principles.
Evaluate the derivative of f (x) = xn wrt x from definition of derivative. Hence find the derivative of wrt x.
Find the derivative of sin x wrt x from first principles.
Differentiate ax wrt x from first principles.
Differentiate sin (log x) wrt x from first principles.
Find dy/dx for the functions.
Find the expression for dy/dx for the following implicit function.
x3 + y3 – 3xy = 1.
Find dy/dx if