Solve 616164x3164

$$616164x3164$$

Evaluate

$$616164x_{3164}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9999}616164\\\underline{\times\phantom{999999}3164}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 616164 with 4. Write the result 2464656 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}616164\\\underline{\times\phantom{999999}3164}\\\phantom{\times999}2464656\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 616164 with 6. Write the result 3696984 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}616164\\\underline{\times\phantom{999999}3164}\\\phantom{\times999}2464656\\\phantom{\times99}3696984\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 616164 with 1. Write the result 616164 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}616164\\\underline{\times\phantom{999999}3164}\\\phantom{\times999}2464656\\\phantom{\times99}3696984\phantom{9}\\\phantom{\times99}616164\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 616164 with 3. Write the result 1848492 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}616164\\\underline{\times\phantom{999999}3164}\\\phantom{\times999}2464656\\\phantom{\times99}3696984\phantom{9}\\\phantom{\times99}616164\phantom{99}\\\underline{\phantom{\times}1848492\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9999}616164\\\underline{\times\phantom{999999}3164}\\\phantom{\times999}2464656\\\phantom{\times99}3696984\phantom{9}\\\phantom{\times99}616164\phantom{99}\\\underline{\phantom{\times}1848492\phantom{999}}\\\phantom{\times}1949542896\end{array}$$

Differentiate w.r.t. x_3164

$$616164$$

Steps Using Definition of a Derivative

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

$$616164x_{3164}^{1-1}$$

Subtract 1 from 1.

$$616164x_{3164}^{0}$$

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

$$616164\times 1$$

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

$$616164$$