Solve 65x65

$$65x65$$

Evaluate

$$65x_{65}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times99}65\\\underline{\times\phantom{99}65}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 65 with 5. Write the result 325 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}65\\\underline{\times\phantom{99}65}\\\phantom{\times9}325\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 65 with 6. Write the result 390 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times99}65\\\underline{\times\phantom{99}65}\\\phantom{\times9}325\\\underline{\phantom{\times}390\phantom{9}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times99}65\\\underline{\times\phantom{99}65}\\\phantom{\times9}325\\\underline{\phantom{\times}390\phantom{9}}\\\phantom{\times}4225\end{array}$$

Differentiate w.r.t. x_65

$$65$$

Steps Using Definition of a Derivative

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

$$65x_{65}^{1-1}$$

Subtract 1 from 1.

$$65x_{65}^{0}$$

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

$$65\times 1$$

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

$$65$$