Solve 78x1245=

$$78x1245=$$

Evaluate

$$78x_{1245}$$

Steps For Long Multiplication

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

$$\begin{array}{c}\phantom{\times999}78\\\underline{\times\phantom{9}1245}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 78 with 5. Write the result 390 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}78\\\underline{\times\phantom{9}1245}\\\phantom{\times99}390\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 78 with 4. Write the result 312 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}78\\\underline{\times\phantom{9}1245}\\\phantom{\times99}390\\\phantom{\times9}312\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 78 with 2. Write the result 156 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}78\\\underline{\times\phantom{9}1245}\\\phantom{\times99}390\\\phantom{\times9}312\phantom{9}\\\phantom{\times}156\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 78 with 1. Write the result 78 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}78\\\underline{\times\phantom{9}1245}\\\phantom{\times99}390\\\phantom{\times9}312\phantom{9}\\\phantom{\times}156\phantom{99}\\\underline{\phantom{\times}78\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times999}78\\\underline{\times\phantom{9}1245}\\\phantom{\times99}390\\\phantom{\times9}312\phantom{9}\\\phantom{\times}156\phantom{99}\\\underline{\phantom{\times}78\phantom{999}}\\\phantom{\times}97110\end{array}$$

Differentiate w.r.t. x_1245

$$78$$

Steps Using Definition of a Derivative

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

$$78x_{1245}^{1-1}$$

Subtract 1 from 1.

$$78x_{1245}^{0}$$

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

$$78\times 1$$

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

$$78$$