Let y = f (x) be a differentiable function of x. Then its derivative f ‘(x), is called the first derivative of f. The fist derivative, in general is itself a function of x which can further be differentiated with respect to x. The resulting derivative, if it exists, is called the second derivative of f. It is denoted by f ‘’(x) (read “f double prime of x”) . Similarly, if the second derivative is differentiable, its derivative is called the third derivative, written f ‘’’(x). Continuing in this way, we get higher-order derivatives. The process of finding higher-order derivatives of a function is called successive differentiation.

Some other notations for higher-order derivatives are:

First derivative        :         y ', y1, dy/dx, d/dx [f (x)]

Second derivative   :          y ' ', y₂' d²y/dx²' d²/dx² [f (x)]

Third derivative       :          y ' ' ', y₃, d³y/dx³, d³/dx³ [f (x)].


nth derivative          :          y⁽ⁿ⁾ , y_n, dⁿy/dxⁿ, dⁿ/dxⁿ [f (x)].


For more help in Successive Differentiation click the button below to submit your homework assignment