Solve 7889x5279

$$7889x5279$$

Evaluate

$$7889x_{5279}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9999}7889\\\underline{\times\phantom{9999}5279}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 7889 with 9. Write the result 71001 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7889\\\underline{\times\phantom{9999}5279}\\\phantom{\times999}71001\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 7889 with 7. Write the result 55223 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7889\\\underline{\times\phantom{9999}5279}\\\phantom{\times999}71001\\\phantom{\times99}55223\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 7889 with 2. Write the result 15778 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7889\\\underline{\times\phantom{9999}5279}\\\phantom{\times999}71001\\\phantom{\times99}55223\phantom{9}\\\phantom{\times9}15778\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 7889 with 5. Write the result 39445 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9999}7889\\\underline{\times\phantom{9999}5279}\\\phantom{\times999}71001\\\phantom{\times99}55223\phantom{9}\\\phantom{\times9}15778\phantom{99}\\\underline{\phantom{\times}39445\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9999}7889\\\underline{\times\phantom{9999}5279}\\\phantom{\times999}71001\\\phantom{\times99}55223\phantom{9}\\\phantom{\times9}15778\phantom{99}\\\underline{\phantom{\times}39445\phantom{999}}\\\phantom{\times}41646031\end{array}$$

Differentiate w.r.t. x_5279

$$7889$$

Steps Using Definition of a Derivative

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

$$7889x_{5279}^{1-1}$$

Subtract 1 from 1.

$$7889x_{5279}^{0}$$

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

$$7889\times 1$$

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

$$7889$$