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Differentiate w.r.t. x
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4\times 2x^{4-1}+3\left(-4\right)x^{3-1}
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}.
8x^{4-1}+3\left(-4\right)x^{3-1}
Multiply 4 times 2.
8x^{3}+3\left(-4\right)x^{3-1}
Subtract 1 from 4.
8x^{3}-12x^{3-1}
Multiply 3 times -4.
8x^{3}-12x^{2}
Subtract 1 from 3.