Solve 2525x255

$$2525x255$$

Evaluate

$$2525x_{255}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}2525\\\underline{\times\phantom{999}255}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 2525 with 5. Write the result 12625 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}2525\\\underline{\times\phantom{999}255}\\\phantom{\times9}12625\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 2525 with 5. Write the result 12625 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}2525\\\underline{\times\phantom{999}255}\\\phantom{\times9}12625\\\phantom{\times}12625\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 2525 with 2. Write the result 5050 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}2525\\\underline{\times\phantom{999}255}\\\phantom{\times9}12625\\\phantom{\times}12625\phantom{9}\\\underline{\phantom{\times}5050\phantom{99}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}2525\\\underline{\times\phantom{999}255}\\\phantom{\times9}12625\\\phantom{\times}12625\phantom{9}\\\underline{\phantom{\times}5050\phantom{99}}\\\phantom{\times}643875\end{array}$$

Differentiate w.r.t. x_255

$$2525$$

Steps Using Definition of a Derivative

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

$$2525x_{255}^{1-1}$$

Subtract 1 from 1.

$$2525x_{255}^{0}$$

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

$$2525\times 1$$

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

$$2525$$