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Differentiate w.r.t. w
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w^{2}+2w-4+w+7
Combine -5w^{2} and 6w^{2} to get w^{2}.
w^{2}+3w-4+7
Combine 2w and w to get 3w.
w^{2}+3w+3
Add -4 and 7 to get 3.
\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}+2w-4+w+7)
Combine -5w^{2} and 6w^{2} to get w^{2}.
\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}+3w-4+7)
Combine 2w and w to get 3w.
\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}+3w+3)
Add -4 and 7 to get 3.
2w^{2-1}+3w^{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}.
2w^{1}+3w^{1-1}
Subtract 1 from 2.
2w^{1}+3w^{0}
Subtract 1 from 1.
2w+3w^{0}
For any term t, t^{1}=t.
2w+3\times 1
For any term t except 0, t^{0}=1.
2w+3
For any term t, t\times 1=t and 1t=t.