Solve 22x^7-83x^4+2x+5

$$22 x ^ { 7 } - 83 x ^ { 4 } + 2 x + 5$$

Differentiate w.r.t. x

$$154x^{6}-332x^{3}+2$$

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}.

$$7\times 22x^{7-1}+4\left(-83\right)x^{4-1}+2x^{1-1}$$

Multiply 7 times 22.

$$154x^{7-1}+4\left(-83\right)x^{4-1}+2x^{1-1}$$

Subtract 1 from 7.

$$154x^{6}+4\left(-83\right)x^{4-1}+2x^{1-1}$$

Multiply 4 times -83.

$$154x^{6}-332x^{4-1}+2x^{1-1}$$

Subtract 1 from 4.

$$154x^{6}-332x^{3}+2x^{1-1}$$

Subtract 1 from 1.

$$154x^{6}-332x^{3}+2x^{0}$$

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

$$154x^{6}-332x^{3}+2\times 1$$

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

$$154x^{6}-332x^{3}+2$$

Evaluate

$$22x^{7}-83x^{4}+2x+5$$