Solve 12x15

$$12x15$$

Evaluate

$$12x_{15}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times9}12\\\underline{\times\phantom{9}15}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 12 with 5. Write the result 60 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}12\\\underline{\times\phantom{9}15}\\\phantom{\times9}60\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 12 with 1. Write the result 12 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times9}12\\\underline{\times\phantom{9}15}\\\phantom{\times9}60\\\underline{\phantom{\times}12\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times9}12\\\underline{\times\phantom{9}15}\\\phantom{\times9}60\\\underline{\phantom{\times}12\phantom{9}}\\\phantom{\times}180\end{array}$$

Differentiate w.r.t. x_15

$$12$$

Steps Using Definition of a Derivative

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

$$12x_{15}^{1-1}$$

Subtract 1 from 1.

$$12x_{15}^{0}$$

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

$$12\times 1$$

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

$$12$$