Solve 4y^2-12y^2+9-9y^2+4

$$4 { y }^{ 2 } -12 { y }^{ 2 } +9-9 { y }^{ 2 } +4$$

Evaluate

$$13-17y^{2}$$

Solution Steps

Combine 4y^{2} and -12y^{2} to get -8y^{2}.

$$-8y^{2}+9-9y^{2}+4$$

Combine -8y^{2} and -9y^{2} to get -17y^{2}.

$$-17y^{2}+9+4$$

Add 9 and 4 to get 13.

$$-17y^{2}+13$$

Differentiate w.r.t. y

$$-34y$$

Steps Using Derivative Rule for Sum

Combine 4y^{2} and -12y^{2} to get -8y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-8y^{2}+9-9y^{2}+4)$$

Combine -8y^{2} and -9y^{2} to get -17y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-17y^{2}+9+4)$$

Add 9 and 4 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-17y^{2}+13)$$

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}.

$$2\left(-17\right)y^{2-1}$$

Multiply 2 times -17.

$$-34y^{2-1}$$

Subtract 1 from 2.

$$-34y^{1}$$

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

$$-34y$$