Solve x^7/x^-1

$$\frac{ { x }^{ 7 } }{ { x }^{ -1 } }$$

Differentiate w.r.t. x

$$8x^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{7-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8})$$

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}.

$$8x^{8-1}$$

Do the arithmetic.

$$8x^{7}$$

Evaluate

$$x^{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 7 to get 8.

$$x^{8}$$