Solve 2^-2x^0y^-3

$$2 ^ { - 2 } x ^ { 0 } y ^ { - 3 }$$

Evaluate

$$\frac{1}{4y^{3}}$$

Solution Steps

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

$$\frac{1}{4}x^{0}y^{-3}$$

Calculate x to the power of 0 and get 1.

$$\frac{1}{4}\times 1y^{-3}$$

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

$$\frac{1}{4}y^{-3}$$

Differentiate w.r.t. y

$$-\frac{3}{4y^{4}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{4}x^{0}y^{-3})$$

Calculate x to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{4}\times 1y^{-3})$$

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{4}y^{-3})$$

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

$$-3\times \frac{1}{4}y^{-3-1}$$

Multiply -3 times \frac{1}{4}.

$$-\frac{3}{4}y^{-3-1}$$

Subtract 1 from -3.

$$-\frac{3}{4}y^{-4}$$