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Differentiate w.r.t. x
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9x^{9-1}+7\times 7x^{7-1}
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}.
9x^{8}+7\times 7x^{7-1}
Subtract 1 from 9.
9x^{8}+49x^{7-1}
Multiply 7 times 7.
9x^{8}+49x^{6}
Subtract 1 from 7.