Solve 789x1483=

$$789x1483=$$

Evaluate

$$789x_{1483}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9999}789\\\underline{\times\phantom{999}1483}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 789 with 3. Write the result 2367 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}789\\\underline{\times\phantom{999}1483}\\\phantom{\times999}2367\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 789 with 8. Write the result 6312 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}789\\\underline{\times\phantom{999}1483}\\\phantom{\times999}2367\\\phantom{\times99}6312\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 789 with 4. Write the result 3156 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}789\\\underline{\times\phantom{999}1483}\\\phantom{\times999}2367\\\phantom{\times99}6312\phantom{9}\\\phantom{\times9}3156\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 789 with 1. Write the result 789 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}789\\\underline{\times\phantom{999}1483}\\\phantom{\times999}2367\\\phantom{\times99}6312\phantom{9}\\\phantom{\times9}3156\phantom{99}\\\underline{\phantom{\times9}789\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9999}789\\\underline{\times\phantom{999}1483}\\\phantom{\times999}2367\\\phantom{\times99}6312\phantom{9}\\\phantom{\times9}3156\phantom{99}\\\underline{\phantom{\times9}789\phantom{999}}\\\phantom{\times}1170087\end{array}$$

Differentiate w.r.t. x_1483

$$789$$

Steps Using Definition of a Derivative

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

$$789x_{1483}^{1-1}$$

Subtract 1 from 1.

$$789x_{1483}^{0}$$

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

$$789\times 1$$

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

$$789$$