Use the rules of exponents to simplify the expression.
\frac{4^{1}\sqrt{x}}{8^{1}\sqrt[3]{x}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{4^{1}x^{\frac{1}{2}-\frac{1}{3}}}{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{4^{1}\sqrt[6]{x}}{8^{1}}
Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.
\frac{1}{2}\sqrt[6]{x}
Differentiate w.r.t. x
\frac{1}{12x^{\frac{5}{6}}}
Solution Steps
\frac { 4 x ^ { 1 / 2 } } { 8 x ^ { 1 / 3 } }
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
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}.
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.
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}.