Solve f^-1*f^-1*f^5

$$f ^ { - 1 } \cdot f ^ { - 1 } \cdot f ^ { 5 }$$

Evaluate

$$f^{3}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{1}{f}\times \frac{1}{f}f^{5}$$

Use the Multiplication Rule for Exponents.

$$f^{-1-1+5}$$

Add the exponents -1 and -1.

$$f^{-2+5}$$

Add the exponents -2 and 5.

$$f^{3}$$

Differentiate w.r.t. f

$$3f^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -1 and -1 to get -2.

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

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{3})$$

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

$$3f^{3-1}$$

Subtract 1 from 3.

$$3f^{2}$$