Solve x^frac{17{6}}*x^-frac{11{6}}*x^-frac{17{6}}

$$x ^ { \frac { 17 } { 6 } } \cdot x ^ { - \frac { 11 } { 6 } } \cdot x ^ { - \frac { 17 } { 6 } }$$

Evaluate

$$\frac{1}{x^{\frac{11}{6}}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{\frac{17}{6}}x^{-\frac{11}{6}}x^{-\frac{17}{6}}$$

Use the Multiplication Rule for Exponents.

$$x^{\frac{17-11-17}{6}}$$

Add the exponents \frac{17}{6} and -\frac{11}{6}.

$$x^{1-\frac{17}{6}}$$

Add the exponents 1 and -\frac{17}{6}.

$$x^{-\frac{11}{6}}$$

Differentiate w.r.t. x

$$-\frac{11}{6x^{\frac{17}{6}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{17}{6} and -\frac{11}{6} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}x^{-\frac{17}{6}})$$

To multiply powers of the same base, add their exponents. Add 1 and -\frac{17}{6} to get -\frac{11}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-\frac{11}{6}})$$

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

$$-\frac{11}{6}x^{-\frac{11}{6}-1}$$

Subtract 1 from -\frac{11}{6}.

$$-\frac{11}{6}x^{-\frac{17}{6}}$$