Solve 4x^3/2/2x^1/3

$$\frac { 4 x ^ { 3 / 2 } } { 2 x ^ { 1 / 3 } }$$

Evaluate

$$2x^{\frac{7}{6}}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}x^{\frac{3}{2}}}{2^{1}\sqrt[3]{x}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{4^{1}x^{\frac{3}{2}-\frac{1}{3}}}{2^{1}}$$

Subtract \frac{1}{3} from \frac{3}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{4^{1}x^{\frac{7}{6}}}{2^{1}}$$

Divide 4 by 2.

$$2x^{\frac{7}{6}}$$

Differentiate w.r.t. x

$$\frac{7\sqrt[6]{x}}{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{2}x^{\frac{3}{2}-\frac{1}{3}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{\frac{7}{6}})$$

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}.

$$\frac{7}{6}\times 2x^{\frac{7}{6}-1}$$

Do the arithmetic.

$$\frac{7}{3}\sqrt[6]{x}$$