Solve 11x11

$$11x11$$

Evaluate

$$11x_{11}$$

Steps For Long Multiplication

First line up the numbers vertically and match the places from the right like this.

$$\begin{array}{c}\phantom{\times9}11\\\underline{\times\phantom{9}11}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 11 with 1. Write the result 11 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}11\\\underline{\times\phantom{9}11}\\\phantom{\times9}11\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 11 with 1. Write the result 11 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}11\\\underline{\times\phantom{9}11}\\\phantom{\times9}11\\\underline{\phantom{\times}11\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9}11\\\underline{\times\phantom{9}11}\\\phantom{\times9}11\\\underline{\phantom{\times}11\phantom{9}}\\\phantom{\times}121\end{array}$$

Differentiate w.r.t. x_11

$$11$$

Steps Using Definition of a Derivative

The derivative of ax^{n} is nax^{n-1}.

$$11x_{11}^{1-1}$$

Subtract 1 from 1.

$$11x_{11}^{0}$$

For any term t except 0, t^{0}=1.

$$11\times 1$$

For any term t, t\times 1=t and 1t=t.

$$11$$