Solve 600x642

$$600x642$$

Evaluate

$$600x_{642}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times999}600\\\underline{\times\phantom{999}642}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 600 with 2. Write the result 1200 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}600\\\underline{\times\phantom{999}642}\\\phantom{\times99}1200\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 600 with 4. Write the result 2400 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}600\\\underline{\times\phantom{999}642}\\\phantom{\times99}1200\\\phantom{\times9}2400\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 600 with 6. Write the result 3600 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}600\\\underline{\times\phantom{999}642}\\\phantom{\times99}1200\\\phantom{\times9}2400\phantom{9}\\\underline{\phantom{\times}3600\phantom{99}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times999}600\\\underline{\times\phantom{999}642}\\\phantom{\times99}1200\\\phantom{\times9}2400\phantom{9}\\\underline{\phantom{\times}3600\phantom{99}}\\\phantom{\times}385200\end{array}$$

Differentiate w.r.t. x_642

$$600$$

Steps Using Definition of a Derivative

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

$$600x_{642}^{1-1}$$

Subtract 1 from 1.

$$600x_{642}^{0}$$

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

$$600\times 1$$

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

$$600$$