Solve 2+8v-v^4+15v^2

$$2 + 8 v - v ^ { 4 } + 15 v ^ { 2 }$$

Differentiate w.r.t. v

$$8+30v-4v^{3}$$

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}.

$$8v^{1-1}+4\left(-1\right)v^{4-1}+2\times 15v^{2-1}$$

Subtract 1 from 1.

$$8v^{0}+4\left(-1\right)v^{4-1}+2\times 15v^{2-1}$$

Multiply 4 times -1.

$$8v^{0}-4v^{4-1}+2\times 15v^{2-1}$$

Subtract 1 from 4.

$$8v^{0}-4v^{3}+2\times 15v^{2-1}$$

Multiply 4 times -1.

$$8v^{0}-4v^{3}+30v^{2-1}$$

Subtract 1 from 2.

$$8v^{0}-4v^{3}+30v^{1}$$

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

$$8v^{0}-4v^{3}+30v$$

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

$$8\times 1-4v^{3}+30v$$

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

$$8-4v^{3}+30v$$

Evaluate

$$2+8v+15v^{2}-v^{4}$$