Solve 45x14=

$$45x14=$$

Evaluate

$$45x_{14}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9}45\\\underline{\times\phantom{9}14}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 45 with 4. Write the result 180 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}45\\\underline{\times\phantom{9}14}\\\phantom{\times}180\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 45 with 1. Write the result 45 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}45\\\underline{\times\phantom{9}14}\\\phantom{\times}180\\\underline{\phantom{\times}45\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9}45\\\underline{\times\phantom{9}14}\\\phantom{\times}180\\\underline{\phantom{\times}45\phantom{9}}\\\phantom{\times}630\end{array}$$

Differentiate w.r.t. x_14

$$45$$

Steps Using Definition of a Derivative

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

$$45x_{14}^{1-1}$$

Subtract 1 from 1.

$$45x_{14}^{0}$$

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

$$45\times 1$$

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

$$45$$