Solve (2y^3)(2y)

$$( 2 y ^ { 3 } ) ( 2 y )$$

Evaluate

$$4y^{4}$$

Solution Steps

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

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

Multiply 2 and 2 to get 4.

$$4y^{4}$$

Differentiate w.r.t. y

$$16y^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 2 to get 4.

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

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

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

Multiply 4 times 4.

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

Subtract 1 from 4.

$$16y^{3}$$