Solve 120x1000

$$120 x 1000$$

Evaluate

$$120x_{1000}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times999}120\\\underline{\times\phantom{99}1000}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 120 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}120\\\underline{\times\phantom{99}1000}\\\phantom{\times999999}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 120 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}120\\\underline{\times\phantom{99}1000}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 120 with 0. Write the result 0 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}120\\\underline{\times\phantom{99}1000}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\phantom{\times9999}0\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 120 with 1. Write the result 120 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}120\\\underline{\times\phantom{99}1000}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\phantom{\times9999}0\phantom{99}\\\underline{\phantom{\times}120\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times999}120\\\underline{\times\phantom{99}1000}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\phantom{\times9999}0\phantom{99}\\\underline{\phantom{\times}120\phantom{999}}\\\phantom{\times}120000\end{array}$$

Differentiate w.r.t. x_1000

$$120$$

Steps Using Definition of a Derivative

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

$$120x_{1000}^{1-1}$$

Subtract 1 from 1.

$$120x_{1000}^{0}$$

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

$$120\times 1$$

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

$$120$$