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Differentiate w.r.t. a
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\frac{\mathrm{d}}{\mathrm{d}a}(531441-3a^{4}+8a^{3}-4a^{2})
Calculate 9 to the power of 6 and get 531441.
4\left(-3\right)a^{4-1}+3\times 8a^{3-1}+2\left(-4\right)a^{2-1}
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}.
-12a^{4-1}+3\times 8a^{3-1}+2\left(-4\right)a^{2-1}
Multiply 4 times -3.
-12a^{3}+3\times 8a^{3-1}+2\left(-4\right)a^{2-1}
Subtract 1 from 4.
-12a^{3}+24a^{3-1}+2\left(-4\right)a^{2-1}
Multiply 3 times 8.
-12a^{3}+24a^{2}+2\left(-4\right)a^{2-1}
Subtract 1 from 3.
-12a^{3}+24a^{2}-8a^{2-1}
Multiply 3 times 8.
-12a^{3}+24a^{2}-8a^{1}
Subtract 1 from 2.
-12a^{3}+24a^{2}-8a
For any term t, t^{1}=t.
531441-3a^{4}+8a^{3}-4a^{2}
Calculate 9 to the power of 6 and get 531441.