Solve 2x^1/6*2x^-7/6

$$2 x ^ { 1 / 6 } \times 2 x ^ { - 7 / 6 }$$

Evaluate

$$\frac{4}{x}$$

Solution Steps

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

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

Multiply 2 and 2 to get 4.

$$4x^{-1}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{-1}\times 2)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-1})$$

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

$$-4x^{-1-1}$$

Subtract 1 from -1.

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