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Differentiate w.r.t. x_11
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\begin{array}{c}\phantom{\times9}13\\\underline{\times\phantom{9}11}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times9}13\\\underline{\times\phantom{9}11}\\\phantom{\times9}13\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 13 with 1. Write the result 13 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times9}13\\\underline{\times\phantom{9}11}\\\phantom{\times9}13\\\underline{\phantom{\times}13\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 13 with 1. Write the result 13 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times9}13\\\underline{\times\phantom{9}11}\\\phantom{\times9}13\\\underline{\phantom{\times}13\phantom{9}}\\\phantom{\times}143\end{array}
Now add the intermediate results to get final answer.
13x_{11}^{1-1}
The derivative of ax^{n} is nax^{n-1}.
13x_{11}^{0}
Subtract 1 from 1.
13\times 1
For any term t except 0, t^{0}=1.
13
For any term t, t\times 1=t and 1t=t.