Solve (-y^2)(-5y)(-9y^5)

$$( - y ^ { 2 } ) ( - 5 y ) ( - 9 y ^ { 5 } )$$

Evaluate

$$-45y^{8}$$

Solution Steps

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

$$\left(-y^{2}\right)\left(-5\right)y^{6}\left(-9\right)$$

Multiply -5 and -9 to get 45.

$$\left(-y^{2}\right)\times 45y^{6}$$

Multiply -1 and 45 to get -45.

$$-45y^{2}y^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-45y^{8}$$

Differentiate w.r.t. y

$$-360y^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-y^{2}\right)\left(-5\right)y^{6}\left(-9\right))$$

Multiply -5 and -9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-y^{2}\right)\times 45y^{6})$$

Multiply -1 and 45 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-45y^{2}y^{6})$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-45y^{8})$$

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

$$8\left(-45\right)y^{8-1}$$

Multiply 8 times -45.

$$-360y^{8-1}$$

Subtract 1 from 8.

$$-360y^{7}$$