Solve -12-5w+4w^9-10w^4

$$- 12 - 5 w + 4 w ^ { 9 } - 10 w ^ { 4 }$$

Differentiate w.r.t. w

$$36w^{8}-40w^{3}-5$$

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}.

$$-5w^{1-1}+9\times 4w^{9-1}+4\left(-10\right)w^{4-1}$$

Subtract 1 from 1.

$$-5w^{0}+9\times 4w^{9-1}+4\left(-10\right)w^{4-1}$$

Multiply 9 times 4.

$$-5w^{0}+36w^{9-1}+4\left(-10\right)w^{4-1}$$

Subtract 1 from 9.

$$-5w^{0}+36w^{8}+4\left(-10\right)w^{4-1}$$

Multiply 9 times 4.

$$-5w^{0}+36w^{8}-40w^{4-1}$$

Subtract 1 from 4.

$$-5w^{0}+36w^{8}-40w^{3}$$

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

$$-5+36w^{8}-40w^{3}$$

Evaluate

$$4w^{9}-10w^{4}-5w-12$$