Solve 3y^2+9y^2-2y^2

$$3 y ^ { 2 } + 9 y ^ { 2 } - 2 y ^ { 2 }$$

Evaluate

$$10y^{2}$$

Solution Steps

Combine 3y^{2} and 9y^{2} to get 12y^{2}.

$$12y^{2}-2y^{2}$$

Combine 12y^{2} and -2y^{2} to get 10y^{2}.

$$10y^{2}$$

Differentiate w.r.t. y

$$20y$$

Steps Using Definition of a Derivative

Combine 3y^{2} and 9y^{2} to get 12y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(12y^{2}-2y^{2})$$

Combine 12y^{2} and -2y^{2} to get 10y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(10y^{2})$$

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

$$2\times 10y^{2-1}$$

Multiply 2 times 10.

$$20y^{2-1}$$

Subtract 1 from 2.

$$20y^{1}$$

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

$$20y$$