Solve 14s+8+3s^8-6s^6

$$14 s + 8 + 3 s ^ { 8 } - 6 s ^ { 6 }$$

Differentiate w.r.t. s

$$24s^{7}-36s^{5}+14$$

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}.

$$14s^{1-1}+8\times 3s^{8-1}+6\left(-6\right)s^{6-1}$$

Subtract 1 from 1.

$$14s^{0}+8\times 3s^{8-1}+6\left(-6\right)s^{6-1}$$

Multiply 8 times 3.

$$14s^{0}+24s^{8-1}+6\left(-6\right)s^{6-1}$$

Subtract 1 from 8.

$$14s^{0}+24s^{7}+6\left(-6\right)s^{6-1}$$

Multiply 8 times 3.

$$14s^{0}+24s^{7}-36s^{6-1}$$

Subtract 1 from 6.

$$14s^{0}+24s^{7}-36s^{5}$$

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

$$14\times 1+24s^{7}-36s^{5}$$

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

$$14+24s^{7}-36s^{5}$$

Evaluate

$$3s^{8}-6s^{6}+14s+8$$