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Differentiate w.r.t. a
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\left(-a^{2}\right)c^{2}\times 6a^{2}
Multiply c and c to get c^{2}.
-6a^{2}c^{2}a^{2}
Multiply -1 and 6 to get -6.
-6a^{4}c^{2}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.