Solve 500x50

$$500x50$$

Evaluate

$$500x_{50}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}500\\\underline{\times\phantom{999}50}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 500 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}500\\\underline{\times\phantom{999}50}\\\phantom{\times99999}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 500 with 5. Write the result 2500 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}500\\\underline{\times\phantom{999}50}\\\phantom{\times99999}0\\\underline{\phantom{\times}2500\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}500\\\underline{\times\phantom{999}50}\\\phantom{\times99999}0\\\underline{\phantom{\times}2500\phantom{9}}\\\phantom{\times}25000\end{array}$$

Differentiate w.r.t. x_50

$$500$$

Steps Using Definition of a Derivative

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

$$500x_{50}^{1-1}$$

Subtract 1 from 1.

$$500x_{50}^{0}$$

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

$$500\times 1$$

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

$$500$$