Solve 15262x4544

$$15262x4544$$

Evaluate

$$15262x_{4544}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times999}15262\\\underline{\times\phantom{9999}4544}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 15262 with 4. Write the result 61048 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}15262\\\underline{\times\phantom{9999}4544}\\\phantom{\times999}61048\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 15262 with 4. Write the result 61048 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}15262\\\underline{\times\phantom{9999}4544}\\\phantom{\times999}61048\\\phantom{\times99}61048\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 15262 with 5. Write the result 76310 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}15262\\\underline{\times\phantom{9999}4544}\\\phantom{\times999}61048\\\phantom{\times99}61048\phantom{9}\\\phantom{\times9}76310\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 15262 with 4. Write the result 61048 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}15262\\\underline{\times\phantom{9999}4544}\\\phantom{\times999}61048\\\phantom{\times99}61048\phantom{9}\\\phantom{\times9}76310\phantom{99}\\\underline{\phantom{\times}61048\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times999}15262\\\underline{\times\phantom{9999}4544}\\\phantom{\times999}61048\\\phantom{\times99}61048\phantom{9}\\\phantom{\times9}76310\phantom{99}\\\underline{\phantom{\times}61048\phantom{999}}\\\phantom{\times}69350528\end{array}$$

Differentiate w.r.t. x_4544

$$15262$$

Steps Using Definition of a Derivative

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

$$15262x_{4544}^{1-1}$$

Subtract 1 from 1.

$$15262x_{4544}^{0}$$

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

$$15262\times 1$$

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

$$15262$$