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Differentiate w.r.t. x
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2ax^{2-1}+5\times 8a^{2}x^{5-1}
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}.
2ax^{1}+5\times 8a^{2}x^{5-1}
Subtract 1 from 2.
2ax^{1}+40a^{2}x^{5-1}
Multiply 5 times 8a^{2}.
2ax^{1}+40a^{2}x^{4}
Subtract 1 from 5.
2ax+40a^{2}x^{4}
For any term t, t^{1}=t.