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Evaluate
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Differentiate w.r.t. a
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\frac{a^{12}}{a^{3}}
Use the rules of exponents to simplify the expression.
a^{12-3}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
a^{9}
Subtract 3 from 12.
\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{12-3})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}a}(a^{9})
Do the arithmetic.
9a^{9-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
9a^{8}
Do the arithmetic.