Solve x^3*x^-7*x

$$x ^ { 3 } \cdot x ^ { - 7 } \cdot x$$

Evaluate

$$\frac{1}{x^{3}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{3}x^{-7}x^{1}$$

Use the Multiplication Rule for Exponents.

$$x^{3-7+1}$$

Add the exponents 3 and -7.

$$x^{-4+1}$$

Add the exponents -4 and 1.

$$x^{-3}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -7 to get -4.

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

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

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

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

$$-3x^{-3-1}$$

Subtract 1 from -3.

$$-3x^{-4}$$