Solve 50x50

$$50x50$$

Evaluate

$$50x_{50}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}50\\\underline{\times\phantom{99}50}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 50 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}50\\\underline{\times\phantom{99}50}\\\phantom{\times9999}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 50 with 5. Write the result 250 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}50\\\underline{\times\phantom{99}50}\\\phantom{\times9999}0\\\underline{\phantom{\times}250\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}50\\\underline{\times\phantom{99}50}\\\phantom{\times9999}0\\\underline{\phantom{\times}250\phantom{9}}\\\phantom{\times}2500\end{array}$$

Differentiate w.r.t. x_50

$$50$$

Steps Using Definition of a Derivative

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

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

Subtract 1 from 1.

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

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

$$50\times 1$$

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

$$50$$