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

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

Evaluate

$$x^{3}$$

Solution Steps

Divide 3 by 3 to get 1.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 1 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})$$

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}.

$$3x^{3-1}$$

Do the arithmetic.

$$3x^{2}$$