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}.

$$4\times 16y^{4-1}$$

Multiply 4 times 16.

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

Subtract 1 from 4.

$$64y^{3}$$