Solve f^0/f^-1*f^-55

$$\frac { f ^ { 0 } } { f ^ { - 1 } \cdot f ^ { - 55 } }$$

Evaluate

$$f^{56}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -55 to get -56.

$$\frac{f^{0}}{f^{-56}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -56 from 0 to get 56.

$$f^{56}$$

Differentiate w.r.t. f

$$56f^{55}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -1 and -55 to get -56.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f^{0}}{f^{-56}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -56 from 0 to get 56.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{56})$$

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

$$56f^{56-1}$$

Subtract 1 from 56.

$$56f^{55}$$