Solve (2y)(3y^2)(6^3)

$$( 2 y ) ( 3 y ^ { 2 } ) ( 6 ^ { 3 } )$$

Evaluate

$$1296y^{3}$$

Solution Steps

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

$$2y^{3}\times 3\times 6^{3}$$

Multiply 2 and 3 to get 6.

$$6y^{3}\times 6^{3}$$

Calculate 6 to the power of 3 and get 216.

$$6y^{3}\times 216$$

Multiply 6 and 216 to get 1296.

$$1296y^{3}$$

Differentiate w.r.t. y

$$3888y^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{3}\times 3\times 6^{3})$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{3}\times 6^{3})$$

Calculate 6 to the power of 3 and get 216.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{3}\times 216)$$

Multiply 6 and 216 to get 1296.

$$\frac{\mathrm{d}}{\mathrm{d}y}(1296y^{3})$$

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

$$3\times 1296y^{3-1}$$

Multiply 3 times 1296.

$$3888y^{3-1}$$

Subtract 1 from 3.

$$3888y^{2}$$