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

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

Evaluate

$$-60y^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$4y^{5}\left(-5\right)\times 3y$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$4y^{6}\left(-5\right)\times 3$$

Multiply 4 and -5 to get -20.

$$-20y^{6}\times 3$$

Multiply -20 and 3 to get -60.

$$-60y^{6}$$

Differentiate w.r.t. y

$$-360y^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{5}\left(-5\right)\times 3y)$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{6}\left(-5\right)\times 3)$$

Multiply 4 and -5 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-20y^{6}\times 3)$$

Multiply -20 and 3 to get -60.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-60y^{6})$$

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

$$6\left(-60\right)y^{6-1}$$

Multiply 6 times -60.

$$-360y^{6-1}$$

Subtract 1 from 6.

$$-360y^{5}$$