Solve y^2+16y+64+y^4

$$y ^ { 2 } + 16 y + 64 + y ^ { 4 }$$

Differentiate w.r.t. y

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

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}.

$$2y^{2-1}+16y^{1-1}+4y^{4-1}$$

Subtract 1 from 2.

$$2y^{1}+16y^{1-1}+4y^{4-1}$$

Subtract 1 from 1.

$$2y^{1}+16y^{0}+4y^{4-1}$$

Subtract 1 from 4.

$$2y^{1}+16y^{0}+4y^{3}$$

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

$$2y+16y^{0}+4y^{3}$$

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

$$2y+16\times 1+4y^{3}$$

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

$$2y+16+4y^{3}$$

Evaluate

$$y^{4}+\left(y+8\right)^{2}$$