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Differentiate w.r.t. b
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\frac{ba}{\left(a-b\right)\left(b-a\right)}
Multiply \frac{b}{a-b} times \frac{a}{b-a} by multiplying numerator times numerator and denominator times denominator.
\frac{ba}{ab-a^{2}-b^{2}+ba}
Apply the distributive property by multiplying each term of a-b by each term of b-a.
\frac{ba}{2ab-a^{2}-b^{2}}
Combine ab and ba to get 2ab.