Solve x^5/x^-8

$$\frac{ { x }^{ 5 } }{ { x }^{ -8 } }$$

Differentiate w.r.t. x

$$13x^{12}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{5-\left(-8\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{13})$$

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}.

$$13x^{13-1}$$

Do the arithmetic.

$$13x^{12}$$

Evaluate

$$x^{13}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -8 from 5 to get 13.

$$x^{13}$$