Solve f/f^0*f^60*f^0

$$\frac { f } { f ^ { 0 } \cdot f ^ { 60 } \cdot f ^ { 0 } }$$

Evaluate

$$\frac{1}{f^{59}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and 60 to get 60.

$$\frac{f}{f^{60}f^{0}}$$

To multiply powers of the same base, add their exponents. Add 60 and 0 to get 60.

$$\frac{f}{f^{60}}$$

Rewrite f^{60} as ff^{59}. Cancel out f in both numerator and denominator.

$$\frac{1}{f^{59}}$$

Differentiate w.r.t. f

$$-\frac{59}{f^{60}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{1}{f^{0}f^{0}}f^{1-60})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{-59})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-59f^{-59-1}$$

Do the arithmetic.

$$-59f^{-60}$$