Solve 4^-2*y^2

$$4 ^ { - 2 } \times y ^ { 2 }$$

Differentiate w.r.t. y

$$\frac{y}{8}$$

Steps Using Definition of a Derivative

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{16}y^{2})$$

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

$$2\times \frac{1}{16}y^{2-1}$$

Multiply 2 times \frac{1}{16}.

$$\frac{1}{8}y^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{8}y^{1}$$

For any term t, t^{1}=t.

$$\frac{1}{8}y$$

Evaluate

$$\frac{y^{2}}{16}$$

Solution Steps

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{1}{16}y^{2}$$