Solve 7y^2-3y^2+2y^2

$$7 y ^ { 2 } - 3 y ^ { 2 } + 2 y ^ { 2 }$$

Evaluate

$$6y^{2}$$

Solution Steps

Combine 7y^{2} and -3y^{2} to get 4y^{2}.

$$4y^{2}+2y^{2}$$

Combine 4y^{2} and 2y^{2} to get 6y^{2}.

$$6y^{2}$$

Differentiate w.r.t. y

$$12y$$

Steps Using Definition of a Derivative

Combine 7y^{2} and -3y^{2} to get 4y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{2}+2y^{2})$$

Combine 4y^{2} and 2y^{2} to get 6y^{2}.

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

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

$$2\times 6y^{2-1}$$

Multiply 2 times 6.

$$12y^{2-1}$$

Subtract 1 from 2.

$$12y^{1}$$

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

$$12y$$