Solve -23w^2+3w-8w^4+2

$$- 23 w ^ { 2 } + 3 w - 8 w ^ { 4 } + 2$$

Differentiate w.r.t. w

$$3-46w-32w^{3}$$

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}.

$$2\left(-23\right)w^{2-1}+3w^{1-1}+4\left(-8\right)w^{4-1}$$

Multiply 2 times -23.

$$-46w^{2-1}+3w^{1-1}+4\left(-8\right)w^{4-1}$$

Subtract 1 from 2.

$$-46w^{1}+3w^{1-1}+4\left(-8\right)w^{4-1}$$

Subtract 1 from 1.

$$-46w^{1}+3w^{0}+4\left(-8\right)w^{4-1}$$

Multiply 1 times 3.

$$-46w^{1}+3w^{0}-32w^{4-1}$$

Subtract 1 from 4.

$$-46w^{1}+3w^{0}-32w^{3}$$

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

$$-46w+3w^{0}-32w^{3}$$

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

$$-46w+3\times 1-32w^{3}$$

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

$$-46w+3-32w^{3}$$

Evaluate

$$2+3w-23w^{2}-8w^{4}$$