Solve (-2)^-2*(x^5)^-2=

$$( - 2 ) ^ { - 2 } \cdot ( x ^ { 5 } ) ^ { - 2 } =$$

Evaluate

$$\frac{1}{4x^{10}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\left(-2\right)^{-2}x^{-10}$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}x^{-10}$$

Differentiate w.r.t. x

$$-\frac{5}{2x^{11}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-2\right)^{-2}x^{-10})$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x^{-10})$$

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

$$-10\times \frac{1}{4}x^{-10-1}$$

Multiply -10 times \frac{1}{4}.

$$-\frac{5}{2}x^{-10-1}$$

Subtract 1 from -10.

$$-\frac{5}{2}x^{-11}$$