Evaluate
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Differentiate w.r.t. x
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\frac{4^{1}\sqrt{x}}{8^{1}\sqrt[3]{x}}
Use the rules of exponents to simplify the expression.
\frac{4^{1}x^{\frac{1}{2}-\frac{1}{3}}}{8^{1}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{4^{1}\sqrt[6]{x}}{8^{1}}
Subtract \frac{1}{3} from \frac{1}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
\frac{1}{2}\sqrt[6]{x}
Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{8}x^{\frac{1}{2}-\frac{1}{3}})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\sqrt[6]{x})
Do the arithmetic.
\frac{1}{6}\times \left(\frac{1}{2}\right)x^{\frac{1}{6}-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{1}{12}x^{-\frac{5}{6}}
Do the arithmetic.