Solve x^5x^-1/x^-3x^-2

$$\frac { x ^ { 5 } x ^ { - 1 } } { x ^ { - 3 } x ^ { - 2 } }$$

Evaluate

$$x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -1 to get 4.

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

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$\frac{x^{4}}{x^{-5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -5 from 4 to get 9.

$$x^{9}$$

Differentiate w.r.t. x

$$9x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and -1 to get 4.

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

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{x^{-5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -5 from 4 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{9})$$

The derivative of ax^{n} is nax^{n-1}.

$$9x^{9-1}$$

Subtract 1 from 9.

$$9x^{8}$$