Solve x^{-2}x^4x^6x^8x^3=

$$x ^ { - 2 } x ^ { 4 } x ^ { 6 } x ^ { 8 } x ^ { 3 } =$$

Evaluate

$$x^{19}$$

Solution Steps

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

$$x^{2}x^{6}x^{8}x^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$x^{8}x^{8}x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$x^{16}x^{3}$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$x^{19}$$

Differentiate w.r.t. x

$$19x^{18}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{6}x^{8}x^{3})$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}x^{8}x^{3})$$

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{16}x^{3})$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{19})$$

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

$$19x^{19-1}$$

Subtract 1 from 19.

$$19x^{18}$$