Solve f^10*f^4/f^5

$$\frac { f ^ { 10 } \times f ^ { 4 } } { f ^ { 5 } }$$

Evaluate

$$f^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{f^{14}}{f^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 14 to get 9.

$$f^{9}$$

Differentiate w.r.t. f

$$9f^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f^{14}}{f^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 14 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{9})$$

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

$$9f^{9-1}$$

Subtract 1 from 9.

$$9f^{8}$$