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Differentiate w.r.t. x
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\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}+x^{2}+10x-4)
Combine -2x^{2} and 3x^{2} to get x^{2}.
5x^{5-1}+2x^{2-1}+10x^{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}.
5x^{4}+2x^{2-1}+10x^{1-1}
Subtract 1 from 5.
5x^{4}+2x^{1}+10x^{1-1}
Subtract 1 from 2.
5x^{4}+2x^{1}+10x^{0}
Subtract 1 from 1.
5x^{4}+2x+10x^{0}
For any term t, t^{1}=t.
5x^{4}+2x+10\times 1
For any term t except 0, t^{0}=1.
5x^{4}+2x+10
For any term t, t\times 1=t and 1t=t.
x^{5}+x^{2}+10x-4
Combine -2x^{2} and 3x^{2} to get x^{2}.