Solve 6y^2(-y^2)

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

Evaluate

$$-6y^{4}$$

Solution Steps

Multiply 6 and -1 to get -6.

$$-6y^{2}y^{2}$$

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

$$-6y^{4}$$

Differentiate w.r.t. y

$$-24y^{3}$$

Steps Using Definition of a Derivative

Multiply 6 and -1 to get -6.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(-6y^{4})$$

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

$$4\left(-6\right)y^{4-1}$$

Multiply 4 times -6.

$$-24y^{4-1}$$

Subtract 1 from 4.

$$-24y^{3}$$