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

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

Evaluate

$$-10y^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$2y^{6}\left(-5\right)$$

Multiply 2 and -5 to get -10.

$$-10y^{6}$$

Differentiate w.r.t. y

$$-60y^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{6}\left(-5\right))$$

Multiply 2 and -5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-10y^{6})$$

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

$$6\left(-10\right)y^{6-1}$$

Multiply 6 times -10.

$$-60y^{6-1}$$

Subtract 1 from 6.

$$-60y^{5}$$