Solve (y^3*(-y)*-y^3)*(-y)

$$( y ^ { 3 } \cdot ( - y ) \cdot - y ^ { 3 } ) \cdot ( - y )$$

Evaluate

$$-y^{8}$$

Solution Steps

Multiply -y and -y to get \left(-y\right)^{2}.

$$y^{3}\left(-y\right)^{2}\left(-y^{3}\right)$$

Calculate -y to the power of 2 and get y^{2}.

$$y^{3}y^{2}\left(-y^{3}\right)$$

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

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

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

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

Differentiate w.r.t. y

$$-8y^{7}$$

Steps Using Definition of a Derivative

Multiply -y and -y to get \left(-y\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3}\left(-y\right)^{2}\left(-y^{3}\right))$$

Calculate -y to the power of 2 and get y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3}y^{2}\left(-y^{3}\right))$$

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

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

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{8}\left(-1\right))$$

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

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

Multiply 8 times -1.

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

Subtract 1 from 8.

$$-8y^{7}$$