Solve d/dyleft(30-yright)(30-y)(y)

$$\frac{d}{d y } \left(30-y \right) (30-y)(y)$$

Evaluate

$$3\left(y-30\right)\left(y-10\right)$$

Steps Using Derivative Rule for Sum

Multiply 30-y and 30-y to get \left(30-y\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(30-y\right)^{2}y)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(30-y\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(900-60y+y^{2}\right)y)$$

Use the distributive property to multiply 900-60y+y^{2} by y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(900y-60y^{2}+y^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$900y^{1-1}+2\left(-60\right)y^{2-1}+3y^{3-1}$$

Subtract 1 from 1.

$$900y^{0}+2\left(-60\right)y^{2-1}+3y^{3-1}$$

Multiply 2 times -60.

$$900y^{0}-120y^{2-1}+3y^{3-1}$$

Subtract 1 from 2.

$$900y^{0}-120y^{1}+3y^{3-1}$$

Subtract 1 from 3.

$$900y^{0}-120y^{1}+3y^{2}$$

For any term t, t^{1}=t.

$$900y^{0}-120y+3y^{2}$$

For any term t except 0, t^{0}=1.

$$900\times 1-120y+3y^{2}$$

For any term t, t\times 1=t and 1t=t.

$$900-120y+3y^{2}$$

Differentiate w.r.t. y

$$6\left(y-20\right)$$