Solve -2y*2y*2y*2y=

$$- 2 y \cdot 2 y \cdot 2 y \cdot 2 y =$$

Evaluate

$$-16y^{4}$$

Solution Steps

Multiply y and y to get y^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-2y^{3}\times 2\times 2\times 2y$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Multiply -2 and 2 to get -4.

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

Multiply -4 and 2 to get -8.

$$-8y^{4}\times 2$$

Multiply -8 and 2 to get -16.

$$-16y^{4}$$

Differentiate w.r.t. y

$$-64y^{3}$$

Steps Using Definition of a Derivative

Multiply y and y to get y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y^{2}\times 2\times 2y\times 2y)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y^{3}\times 2\times 2\times 2y)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y^{4}\times 2\times 2\times 2)$$

Multiply -2 and 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-4y^{4}\times 2\times 2)$$

Multiply -4 and 2 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-8y^{4}\times 2)$$

Multiply -8 and 2 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-16y^{4})$$

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

$$4\left(-16\right)y^{4-1}$$

Multiply 4 times -16.

$$-64y^{4-1}$$

Subtract 1 from 4.

$$-64y^{3}$$