Solve 8332x22

$$8332x22$$

Evaluate

$$8332x_{22}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}8332\\\underline{\times\phantom{9999}22}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 8332 with 2. Write the result 16664 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}8332\\\underline{\times\phantom{9999}22}\\\phantom{\times9}16664\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 8332 with 2. Write the result 16664 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}8332\\\underline{\times\phantom{9999}22}\\\phantom{\times9}16664\\\underline{\phantom{\times}16664\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}8332\\\underline{\times\phantom{9999}22}\\\phantom{\times9}16664\\\underline{\phantom{\times}16664\phantom{9}}\\\phantom{\times}183304\end{array}$$

Differentiate w.r.t. x_22

$$8332$$

Steps Using Definition of a Derivative

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

$$8332x_{22}^{1-1}$$

Subtract 1 from 1.

$$8332x_{22}^{0}$$

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

$$8332\times 1$$

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

$$8332$$