Solve 8y+10+4y^2-9y^5

$$8 y + 10 + 4 y ^ { 2 } - 9 y ^ { 5 }$$

Differentiate w.r.t. y

$$8+8y-45y^{4}$$

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}.

$$8y^{1-1}+2\times 4y^{2-1}+5\left(-9\right)y^{5-1}$$

Subtract 1 from 1.

$$8y^{0}+2\times 4y^{2-1}+5\left(-9\right)y^{5-1}$$

Multiply 2 times 4.

$$8y^{0}+8y^{2-1}+5\left(-9\right)y^{5-1}$$

Subtract 1 from 2.

$$8y^{0}+8y^{1}+5\left(-9\right)y^{5-1}$$

Multiply 2 times 4.

$$8y^{0}+8y^{1}-45y^{5-1}$$

Subtract 1 from 5.

$$8y^{0}+8y^{1}-45y^{4}$$

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

$$8y^{0}+8y-45y^{4}$$

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

$$8\times 1+8y-45y^{4}$$

For any term t, t\times 1=t and 1t=t.

$$8+8y-45y^{4}$$

Evaluate

$$10+8y+4y^{2}-9y^{5}$$