Differentiate w.r.t. a
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3a^{3-1}+2\left(-4\right)a^{2-1}+2a^{1-1}
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}.
3a^{2}+2\left(-4\right)a^{2-1}+2a^{1-1}
Subtract 1 from 3.
3a^{2}-8a^{2-1}+2a^{1-1}
Multiply 2 times -4.
3a^{2}-8a^{1}+2a^{1-1}
Subtract 1 from 2.
3a^{2}-8a^{1}+2a^{0}
Subtract 1 from 1.
3a^{2}-8a+2a^{0}
For any term t, t^{1}=t.
3a^{2}-8a+2\times 1
For any term t except 0, t^{0}=1.
3a^{2}-8a+2
For any term t, t\times 1=t and 1t=t.