Solve (3y)(-5y^2)

$$( 3 y ) ( - 5 y ^ { 2 } )$$

Evaluate

$$-15y^{3}$$

Solution Steps

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

$$3y^{3}\left(-5\right)$$

Multiply 3 and -5 to get -15.

$$-15y^{3}$$

Differentiate w.r.t. y

$$-45y^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{3}\left(-5\right))$$

Multiply 3 and -5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-15y^{3})$$

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

$$3\left(-15\right)y^{3-1}$$

Multiply 3 times -15.

$$-45y^{3-1}$$

Subtract 1 from 3.

$$-45y^{2}$$