Solve x(x^-2)(x^7)

$$x ( x ^ { - 2 } ) ( x ^ { 7 } )$$

Evaluate

$$x^{6}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{1}x^{-2}x^{7}$$

Use the Multiplication Rule for Exponents.

$$x^{1-2+7}$$

Add the exponents 1 and -2.

$$x^{-1+7}$$

Add the exponents -1 and 7.

$$x^{6}$$

Differentiate w.r.t. x

$$6x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

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

To multiply powers of the same base, add their exponents. Add -1 and 7 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6})$$

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

$$6x^{6-1}$$

Subtract 1 from 6.

$$6x^{5}$$