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Differentiate w.r.t. x_0
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Evaluate
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\frac{\mathrm{d}}{\mathrm{d}x_{0}}(0.4x_{0})
Multiply 0.5 and 0.8 to get 0.4.
0.4x_{0}^{1-1}
The derivative of ax^{n} is nax^{n-1}.
0.4x_{0}^{0}
Subtract 1 from 1.
0.4\times 1
For any term t except 0, t^{0}=1.
0.4
For any term t, t\times 1=t and 1t=t.
0.4x_{0}
Multiply 0.5 and 0.8 to get 0.4.