# RD Sharma Solutions Class 12 Higher ORDer Derivatives

## RD Sharma Solutions Class 12 Chapter 12

Let y = f(x), then the derivative of y with respect to x is represented by $\frac{dy}{dx}$ i.e. 1st order derivative of y w.r.t. x.

Now, the derivative of $\frac{dy}{dx}$ w.r.t. x will represent the 2nd order derivative of y i.e. $\frac{d^{2}y}{dx^{2}}$

Further, the derivative of $\frac{d^{2}y}{dx^{2}}$ w.r.t. x will represent the 3rd order derivative of y i.e. $\frac{d^{3}y}{dx^{3}}$. Similarly, we can write the higher order derivatives of y.

Now, if y = f(x), then the other notations for the higher order derivatives:

$\frac{dy}{dx}\;,\;\frac{d^{2}y}{dx^{2}}\;,\;\frac{d^{3}y}{dx^{3}}\;,\;\frac{d^{4}y}{dx^{4}}\;.\;.\;.\;\frac{d^{n}y}{dx^{n}}$ are

$y_{1}\;,\;y_{2}\;,\;y_{3}\;,\;y_{4}\;.\;.\;.\; y_{n}$

$y^{‘}\;,\;y^{”}\;,\;y^{”’}\;,\;y^{””}\;.\;.\;.\;.\;y^{n}$

$Dy\;,\; D^{2}y\;,\;D^{3}y\;,\;D^{4}y\;.\;.\;.\;D^{n}y$

$f^{‘}(x)\;,\; f^{”}(x)\;,\;f^{”’}(x)\;,\;f^{””}(x)\;.\;.\;.\;f^{n}(x)$<

RD Sharma Solutions for Class 12th maths Higher Order Derivatives will help you to prove certain relations involving various order derivatives, for proving relations involving various order derivative of parametric and cartesian functions in a very simplified and easier way. Understand all the important concepts involved in Higher order derivatives in detail with complete exercise wise solved RD Sharma Solutions to accurately answer complex questions asked in competitive exams like JEE Mains and JEE Advanced.

 Higher Order Derivatives Class 12th RD Sharma Exercises Higher Order Derivatives Exercise 12.1

#### Practise This Question

A shopkeeper sold two bats which have a cost price of Rs. 6000 each. He makes a profit of 10% on one of the bats but a loss of 5% on the other bat. Has he made an overall profit or loss?