Differentiate w.r.t. x
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4\times 51x^{4-1}+2\times 3x^{2-1}+x^{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}.
204x^{4-1}+2\times 3x^{2-1}+x^{1-1}
Multiply 4 times 51.
204x^{3}+2\times 3x^{2-1}+x^{1-1}
Subtract 1 from 4.
204x^{3}+6x^{2-1}+x^{1-1}
Multiply 2 times 3.
204x^{3}+6x^{1}+x^{1-1}
Subtract 1 from 2.
204x^{3}+6x^{1}+x^{0}
Subtract 1 from 1.
204x^{3}+6x+x^{0}
For any term t, t^{1}=t.
204x^{3}+6x+1
For any term t except 0, t^{0}=1.