Solve 5y^2-6y-11-6y^2+2y+5

$$5 { y }^{ 2 } -6y-11-6 { y }^{ 2 } +2y+5$$

Evaluate

$$-y^{2}-4y-6$$

Solution Steps

Combine 5y^{2} and -6y^{2} to get -y^{2}.

$$-y^{2}-6y-11+2y+5$$

Combine -6y and 2y to get -4y.

$$-y^{2}-4y-11+5$$

Add -11 and 5 to get -6.

$$-y^{2}-4y-6$$

Differentiate w.r.t. y

$$-2y-4$$

Steps Using Derivative Rule for Sum

Combine 5y^{2} and -6y^{2} to get -y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-y^{2}-6y-11+2y+5)$$

Combine -6y and 2y to get -4y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-y^{2}-4y-11+5)$$

Add -11 and 5 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-y^{2}-4y-6)$$

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}.

$$2\left(-1\right)y^{2-1}-4y^{1-1}$$

Multiply 2 times -1.

$$-2y^{2-1}-4y^{1-1}$$

Subtract 1 from 2.

$$-2y^{1}-4y^{1-1}$$

Subtract 1 from 1.

$$-2y^{1}-4y^{0}$$

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

$$-2y-4y^{0}$$

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

$$-2y-4$$