Solve -5y+13-8y^3+y^2=

$$- 5 y + 13 - 8 y ^ { 3 } + y ^ { 2 } =$$

Differentiate w.r.t. y

$$-24y^{2}+2y-5$$

Steps Using Derivative Rule for Sum

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}.

$$-5y^{1-1}+3\left(-8\right)y^{3-1}+2y^{2-1}$$

Subtract 1 from 1.

$$-5y^{0}+3\left(-8\right)y^{3-1}+2y^{2-1}$$

Multiply 3 times -8.

$$-5y^{0}-24y^{3-1}+2y^{2-1}$$

Subtract 1 from 3.

$$-5y^{0}-24y^{2}+2y^{2-1}$$

Subtract 1 from 2.

$$-5y^{0}-24y^{2}+2y^{1}$$

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

$$-5y^{0}-24y^{2}+2y$$

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

$$-5-24y^{2}+2y$$

Evaluate

$$13-5y+y^{2}-8y^{3}$$