Solve (x)^3(x^-1)^5

$$( x ) ^ { 3 } ( x ^ { - 1 } ) ^ { 5 }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 5 to get -5.

$$x^{3}x^{-5}$$

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

$$x^{-2}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -1 and 5 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{-5})$$

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

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

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

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

Subtract 1 from -2.

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