Solve 7888x555555

$$7888x555555$$

Evaluate

$$7888x_{555555}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 7888 with 5. Write the result 39440 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 7888 with 5. Write the result 39440 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\phantom{\times99}39440\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 7888 with 5. Write the result 39440 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\phantom{\times99}39440\phantom{9}\\\phantom{\times9}39440\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 7888 with 5. Write the result 39440 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\phantom{\times99}39440\phantom{9}\\\phantom{\times9}39440\phantom{99}\\\phantom{\times}39440\phantom{999}\\\end{array}$$

Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 7888 with 5. Write the result 39440 at the end leaving 4 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\phantom{\times99}39440\phantom{9}\\\phantom{\times9}39440\phantom{99}\\\phantom{\times}39440\phantom{999}\\\phantom{\times}39440\phantom{9999}\\\end{array}$$

Now multiply the first number with the 6^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 7888 with 5. Write the result 39440 at the end leaving 5 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\phantom{\times99}39440\phantom{9}\\\phantom{\times9}39440\phantom{99}\\\phantom{\times}39440\phantom{999}\\\phantom{\times}39440\phantom{9999}\\\underline{\phantom{\times}39440\phantom{99999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9999}7888\\\underline{\times\phantom{99}555555}\\\phantom{\times999}39440\\\phantom{\times99}39440\phantom{9}\\\phantom{\times9}39440\phantom{99}\\\phantom{\times}39440\phantom{999}\\\phantom{\times}39440\phantom{9999}\\\underline{\phantom{\times}39440\phantom{99999}}\\\phantom{\times}87250544\end{array}$$

Differentiate w.r.t. x_555555

$$7888$$

Steps Using Definition of a Derivative

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

$$7888x_{555555}^{1-1}$$

Subtract 1 from 1.

$$7888x_{555555}^{0}$$

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

$$7888\times 1$$

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

$$7888$$