Differentiate w.r.t. x
Evaluate
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3\times 8x^{3-1}+2\times 7x^{2-1}+6x^{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}.
24x^{3-1}+2\times 7x^{2-1}+6x^{1-1}
Multiply 3 times 8.
24x^{2}+2\times 7x^{2-1}+6x^{1-1}
Subtract 1 from 3.
24x^{2}+14x^{2-1}+6x^{1-1}
Multiply 2 times 7.
24x^{2}+14x^{1}+6x^{1-1}
Subtract 1 from 2.
24x^{2}+14x^{1}+6x^{0}
Subtract 1 from 1.
24x^{2}+14x+6x^{0}
For any term t, t^{1}=t.
24x^{2}+14x+6\times 1
For any term t except 0, t^{0}=1.
24x^{2}+14x+6
For any term t, t\times 1=t and 1t=t.