Solve (2y)(3y)(5y^4)=

$$( 2 y ) ( 3 y ) ( 5 y ^ { 4 } ) =$$

Evaluate

$$30y^{6}$$

Solution Steps

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

$$2y^{2}\times 3\times 5y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$2y^{6}\times 3\times 5$$

Multiply 2 and 3 to get 6.

$$6y^{6}\times 5$$

Multiply 6 and 5 to get 30.

$$30y^{6}$$

Differentiate w.r.t. y

$$180y^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{2}\times 3\times 5y^{4})$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{6}\times 3\times 5)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{6}\times 5)$$

Multiply 6 and 5 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}y}(30y^{6})$$

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

$$6\times 30y^{6-1}$$

Multiply 6 times 30.

$$180y^{6-1}$$

Subtract 1 from 6.

$$180y^{5}$$