Solve 7-w^9-8w-9w^2

$$7 - w ^ { 9 } - 8 w - 9 w ^ { 2 }$$

Differentiate w.r.t. w

$$-9w^{8}-18w-8$$

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}.

$$9\left(-1\right)w^{9-1}-8w^{1-1}+2\left(-9\right)w^{2-1}$$

Multiply 9 times -1.

$$-9w^{9-1}-8w^{1-1}+2\left(-9\right)w^{2-1}$$

Subtract 1 from 9.

$$-9w^{8}-8w^{1-1}+2\left(-9\right)w^{2-1}$$

Subtract 1 from 1.

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

Multiply 1 times -8.

$$-9w^{8}-8w^{0}-18w^{2-1}$$

Subtract 1 from 2.

$$-9w^{8}-8w^{0}-18w^{1}$$

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

$$-9w^{8}-8w^{0}-18w$$

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

$$-9w^{8}-8-18w$$

Evaluate

$$7-8w-9w^{2}-w^{9}$$