Solve x^-5x^-2x^12/x^6

$${ x }^{ -5 } { x }^{ -2 } \frac{ { x }^{ 12 } }{ { x }^{ 6 } }$$

Evaluate

$$\frac{1}{x}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 12 to get 6.

$$x^{-5}x^{-2}x^{6}$$

To multiply powers of the same base, add their exponents. Add -5 and -2 to get -7.

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

To multiply powers of the same base, add their exponents. Add -7 and 6 to get -1.

$$x^{-1}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 12 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-5}x^{-2}x^{6})$$

To multiply powers of the same base, add their exponents. Add -5 and -2 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-7}x^{6})$$

To multiply powers of the same base, add their exponents. Add -7 and 6 to get -1.

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

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

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

Subtract 1 from -1.

$$-x^{-2}$$