Solve 629x23649

$$629x23649$$

Evaluate

$$629x_{23649}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 629 with 9. Write the result 5661 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\phantom{\times9999}5661\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 629 with 4. Write the result 2516 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\phantom{\times9999}5661\\\phantom{\times999}2516\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 629 with 6. Write the result 3774 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\phantom{\times9999}5661\\\phantom{\times999}2516\phantom{9}\\\phantom{\times99}3774\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 629 with 3. Write the result 1887 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\phantom{\times9999}5661\\\phantom{\times999}2516\phantom{9}\\\phantom{\times99}3774\phantom{99}\\\phantom{\times9}1887\phantom{999}\\\end{array}$$

Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 629 with 2. Write the result 1258 at the end leaving 4 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\phantom{\times9999}5661\\\phantom{\times999}2516\phantom{9}\\\phantom{\times99}3774\phantom{99}\\\phantom{\times9}1887\phantom{999}\\\underline{\phantom{\times}1258\phantom{9999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99999}629\\\underline{\times\phantom{999}23649}\\\phantom{\times9999}5661\\\phantom{\times999}2516\phantom{9}\\\phantom{\times99}3774\phantom{99}\\\phantom{\times9}1887\phantom{999}\\\underline{\phantom{\times}1258\phantom{9999}}\\\phantom{\times}14875221\end{array}$$

Differentiate w.r.t. x_23649

$$629$$

Steps Using Definition of a Derivative

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

$$629x_{23649}^{1-1}$$

Subtract 1 from 1.

$$629x_{23649}^{0}$$

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

$$629\times 1$$

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

$$629$$