Solve (-7y^3)(6y^2)

$$( - 7 y ^ { 3 } ) ( 6 y ^ { 2 } )$$

Evaluate

$$-42y^{5}$$

Solution Steps

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

$$-7y^{5}\times 6$$

Multiply -7 and 6 to get -42.

$$-42y^{5}$$

Differentiate w.r.t. y

$$-210y^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(-7y^{5}\times 6)$$

Multiply -7 and 6 to get -42.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-42y^{5})$$

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

$$5\left(-42\right)y^{5-1}$$

Multiply 5 times -42.

$$-210y^{5-1}$$

Subtract 1 from 5.

$$-210y^{4}$$