Solve 314x12

$$314x12$$

Evaluate

$$314x_{12}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9}314\\\underline{\times\phantom{99}12}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 314 with 2. Write the result 628 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}314\\\underline{\times\phantom{99}12}\\\phantom{\times9}628\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 314 with 1. Write the result 314 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}314\\\underline{\times\phantom{99}12}\\\phantom{\times9}628\\\underline{\phantom{\times}314\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9}314\\\underline{\times\phantom{99}12}\\\phantom{\times9}628\\\underline{\phantom{\times}314\phantom{9}}\\\phantom{\times}3768\end{array}$$

Differentiate w.r.t. x_12

$$314$$

Steps Using Definition of a Derivative

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

$$314x_{12}^{1-1}$$

Subtract 1 from 1.

$$314x_{12}^{0}$$

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

$$314\times 1$$

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

$$314$$