Solve 400x80

$$400x80$$

Evaluate

$$400x_{80}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}400\\\underline{\times\phantom{999}80}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 400 with 0. Write the result 0 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}400\\\underline{\times\phantom{999}80}\\\phantom{\times99999}0\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 400 with 8. Write the result 3200 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}400\\\underline{\times\phantom{999}80}\\\phantom{\times99999}0\\\underline{\phantom{\times}3200\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}400\\\underline{\times\phantom{999}80}\\\phantom{\times99999}0\\\underline{\phantom{\times}3200\phantom{9}}\\\phantom{\times}32000\end{array}$$

Differentiate w.r.t. x_80

$$400$$

Steps Using Definition of a Derivative

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

$$400x_{80}^{1-1}$$

Subtract 1 from 1.

$$400x_{80}^{0}$$

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

$$400\times 1$$

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

$$400$$