Solve 15x75000=

$$15x75000=$$

Evaluate

$$15x_{75000}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\phantom{\times9999999}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\phantom{\times9999999}0\\\phantom{\times999999}0\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 0. Write the result 0 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\phantom{\times9999999}0\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 5. Write the result 75 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\phantom{\times9999999}0\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\phantom{\times99}75\phantom{999}\\\end{array}$$

Now multiply the first number with the 5^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 15 with 7. Write the result 105 at the end leaving 4 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\phantom{\times9999999}0\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\phantom{\times99}75\phantom{999}\\\underline{\phantom{\times}105\phantom{9999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99999}15\\\underline{\times\phantom{99}75000}\\\phantom{\times9999999}0\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\phantom{\times99}75\phantom{999}\\\underline{\phantom{\times}105\phantom{9999}}\\\phantom{\times}1125000\end{array}$$

Differentiate w.r.t. x_75000

$$15$$

Steps Using Definition of a Derivative

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

$$15x_{75000}^{1-1}$$

Subtract 1 from 1.

$$15x_{75000}^{0}$$

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

$$15\times 1$$

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

$$15$$