Solve 70000x114600

$$70000x114600$$

Evaluate

$$70000x_{114600}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 70000 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 70000 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\phantom{\times}0\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 70000 with 6. Write the result 420000 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\phantom{\times}0\phantom{9}\\\phantom{\times}420000\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 70000 with 4. Write the result 280000 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\phantom{\times}0\phantom{9}\\\phantom{\times}420000\phantom{99}\\\phantom{\times}280000\phantom{999}\\\end{array}$$

Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 70000 with 1. Write the result 70000 at the end leaving 4 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\phantom{\times}0\phantom{9}\\\phantom{\times}420000\phantom{99}\\\phantom{\times}280000\phantom{999}\\\phantom{\times}70000\phantom{9999}\\\end{array}$$

Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 70000 with 1. Write the result 70000 at the end leaving 5 spaces to the right like this.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\phantom{\times}0\phantom{9}\\\phantom{\times}420000\phantom{99}\\\phantom{\times}280000\phantom{999}\\\phantom{\times}70000\phantom{9999}\\\underline{\phantom{\times}70000\phantom{99999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times}70000\\\underline{\times\phantom{}114600}\\\phantom{\times}0\\\phantom{\times}0\phantom{9}\\\phantom{\times}420000\phantom{99}\\\phantom{\times}280000\phantom{999}\\\phantom{\times}70000\phantom{9999}\\\underline{\phantom{\times}70000\phantom{99999}}\\\phantom{\times}-567934592\end{array}$$

Differentiate w.r.t. x_114600

$$70000$$

Steps Using Definition of a Derivative

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

$$70000x_{114600}^{1-1}$$

Subtract 1 from 1.

$$70000x_{114600}^{0}$$

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

$$70000\times 1$$

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

$$70000$$