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Evaluate
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Differentiate w.r.t. x
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\frac{18^{1}x^{2}y^{1}}{24^{1}x^{1}y^{1}}
Use the rules of exponents to simplify the expression.
\frac{18^{1}}{24^{1}}x^{2-1}y^{1-1}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{18^{1}}{24^{1}}x^{1}y^{1-1}
Subtract 1 from 2.
\frac{18^{1}}{24^{1}}xy^{0}
Subtract 1 from 1.
\frac{18^{1}}{24^{1}}x
For any number a except 0, a^{0}=1.
\frac{3}{4}x
Reduce the fraction \frac{18}{24} to lowest terms by extracting and canceling out 6.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18y}{24y}x^{2-1})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x^{1})
Do the arithmetic.
\frac{3}{4}x^{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}.
\frac{3}{4}x^{0}
Do the arithmetic.
\frac{3}{4}\times 1
For any term t except 0, t^{0}=1.
\frac{3}{4}
For any term t, t\times 1=t and 1t=t.