Solve f(x)^-2*(5^-1)^2/5*5^-2

$$f \frac { ( x ) ^ { - 2 } \cdot ( 5 ^ { - 1 } ) ^ { 2 } } { 5 \cdot 5 ^ { - 2 } }$$

Evaluate

$$\frac{f}{5x^{2}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$f\times \frac{x^{-2}\times 5^{-2}}{5\times 5^{-2}}$$

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

$$f\times \frac{x^{-2}\times 5^{-2}}{5^{-1}}$$

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

$$f\times \frac{x^{-2}}{5^{1}}$$

Calculate 5 to the power of 1 and get 5.

$$f\times \frac{x^{-2}}{5}$$

Express f\times \frac{x^{-2}}{5} as a single fraction.

$$\frac{fx^{-2}}{5}$$

Differentiate w.r.t. x

$$-\frac{2f}{5x^{3}}$$