Solve 31x49

$$31x49$$

Evaluate

$$31x_{49}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}31\\\underline{\times\phantom{99}49}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 31 with 9. Write the result 279 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}31\\\underline{\times\phantom{99}49}\\\phantom{\times9}279\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 31 with 4. Write the result 124 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}31\\\underline{\times\phantom{99}49}\\\phantom{\times9}279\\\underline{\phantom{\times}124\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}31\\\underline{\times\phantom{99}49}\\\phantom{\times9}279\\\underline{\phantom{\times}124\phantom{9}}\\\phantom{\times}1519\end{array}$$

Differentiate w.r.t. x_49

$$31$$

Steps Using Definition of a Derivative

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

$$31x_{49}^{1-1}$$

Subtract 1 from 1.

$$31x_{49}^{0}$$

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

$$31\times 1$$

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

$$31$$