Solve x^frac{2{3}}divx^-frac{4{3}}

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

Differentiate w.r.t. x

$$2x$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$2x^{2-1}$$

Do the arithmetic.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$

Evaluate

$$x^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{4}{3} from \frac{2}{3} to get 2.

$$x^{2}$$