Solve x^3*x^-7*x^6

$${ x }^{ 3 } \times { x }^{ -7 } \times { x }^{ 6 }$$

Evaluate

$$x^{2}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{3}x^{-7}x^{6}$$

Use the Multiplication Rule for Exponents.

$$x^{3-7+6}$$

Add the exponents 3 and -7.

$$x^{-4+6}$$

Add the exponents -4 and 6.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-4}x^{6})$$

To multiply powers of the same base, add their exponents. Add -4 and 6 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.

$$2x$$