Solve 1000x12

$$1000x12$$

Evaluate

$$1000x_{12}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9}1000\\\underline{\times\phantom{999}12}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 1000 with 2. Write the result 2000 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}1000\\\underline{\times\phantom{999}12}\\\phantom{\times9}2000\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 1000 with 1. Write the result 1000 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}1000\\\underline{\times\phantom{999}12}\\\phantom{\times9}2000\\\underline{\phantom{\times}1000\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9}1000\\\underline{\times\phantom{999}12}\\\phantom{\times9}2000\\\underline{\phantom{\times}1000\phantom{9}}\\\phantom{\times}12000\end{array}$$

Differentiate w.r.t. x_12

$$1000$$

Steps Using Definition of a Derivative

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

$$1000x_{12}^{1-1}$$

Subtract 1 from 1.

$$1000x_{12}^{0}$$

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

$$1000\times 1$$

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

$$1000$$