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Differentiate w.r.t. x_59
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\begin{array}{c}\phantom{\times99}78956\\\underline{\times\phantom{99999}59}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times99}78956\\\underline{\times\phantom{99999}59}\\\phantom{\times9}710604\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 78956 with 9. Write the result 710604 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times99}78956\\\underline{\times\phantom{99999}59}\\\phantom{\times9}710604\\\underline{\phantom{\times}394780\phantom{9}}\\\end{array}
Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 78956 with 5. Write the result 394780 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times99}78956\\\underline{\times\phantom{99999}59}\\\phantom{\times9}710604\\\underline{\phantom{\times}394780\phantom{9}}\\\phantom{\times}4658404\end{array}
Now add the intermediate results to get final answer.
78956x_{59}^{1-1}
The derivative of ax^{n} is nax^{n-1}.
78956x_{59}^{0}
Subtract 1 from 1.
78956\times 1
For any term t except 0, t^{0}=1.
78956
For any term t, t\times 1=t and 1t=t.