Solve x^2x^4-2^3

$$x ^ { 2 } x ^ { 4 - 2 ^ { 3 } }$$

Evaluate

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

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$x^{2}x^{4-8}$$

Subtract 8 from 4 to get -4.

$$x^{2}x^{-4}$$

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$x^{-2}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{4-8})$$

Subtract 8 from 4 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{-4})$$

To multiply powers of the same base, add their exponents. Add 2 and -4 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.

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