Solve x^-6x^5x^3

$$x ^ { - 6 } x ^ { 5 } x ^ { 3 }$$

Evaluate

$$x^{2}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{-6}x^{5}x^{3}$$

Use the Multiplication Rule for Exponents.

$$x^{-6+5+3}$$

Add the exponents -6 and 5.

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

Add the exponents -1 and 3.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -6 and 5 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-1}x^{3})$$

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

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$