Solve f^9*f^3/f^2

$$\frac { f ^ { 9 } \times f ^ { 3 } } { f ^ { 2 } }$$

Evaluate

$$f^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{f^{12}}{f^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 12 to get 10.

$$f^{10}$$

Differentiate w.r.t. f

$$10f^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f^{12}}{f^{2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 12 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{10})$$

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

$$10f^{10-1}$$

Subtract 1 from 10.

$$10f^{9}$$