Solve (5y^4)(3y)

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

Evaluate

$$15y^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply 5 and 3 to get 15.

$$15y^{5}$$

Differentiate w.r.t. y

$$75y^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{5})$$

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

$$5\times 15y^{5-1}$$

Multiply 5 times 15.

$$75y^{5-1}$$

Subtract 1 from 5.

$$75y^{4}$$