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Evaluate
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Differentiate w.r.t. x
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\left(x^{9}\right)^{3}\times \frac{1}{x^{6}}
Use the rules of exponents to simplify the expression.
x^{9\times 3}x^{6\left(-1\right)}
To raise a power to another power, multiply the exponents.
x^{27}x^{6\left(-1\right)}
Multiply 9 times 3.
x^{27}x^{-6}
Multiply 6 times -1.
x^{27-6}
To multiply powers of the same base, add their exponents.
x^{21}
Add the exponents 27 and -6.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{27}}{x^{6}})
To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{21})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 27 to get 21.
21x^{21-1}
The derivative of ax^{n} is nax^{n-1}.
21x^{20}
Subtract 1 from 21.