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

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

Evaluate

$$15y^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$3y^{9}\times 5$$

Multiply 3 and 5 to get 15.

$$15y^{9}$$

Differentiate w.r.t. y

$$135y^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{9}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{9})$$

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

$$9\times 15y^{9-1}$$

Multiply 9 times 15.

$$135y^{9-1}$$

Subtract 1 from 9.

$$135y^{8}$$