Solve 252x600

$$252x600$$

Evaluate

$$252x_{600}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times999}252\\\underline{\times\phantom{999}600}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 252 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}252\\\underline{\times\phantom{999}600}\\\phantom{\times999999}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 252 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}252\\\underline{\times\phantom{999}600}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 252 with 6. Write the result 1512 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}252\\\underline{\times\phantom{999}600}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\underline{\phantom{\times}1512\phantom{99}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times999}252\\\underline{\times\phantom{999}600}\\\phantom{\times999999}0\\\phantom{\times99999}0\phantom{9}\\\underline{\phantom{\times}1512\phantom{99}}\\\phantom{\times}151200\end{array}$$

Differentiate w.r.t. x_600

$$252$$

Steps Using Definition of a Derivative

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

$$252x_{600}^{1-1}$$

Subtract 1 from 1.

$$252x_{600}^{0}$$

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

$$252\times 1$$

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

$$252$$