Solve x-202x^7+10x+1

$$x - 202 x ^ { 7 } + 10 x + 1$$

Differentiate w.r.t. x

$$11-1414x^{6}$$

Steps Using Derivative Rule for Sum

Combine x and 10x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x-202x^{7}+1)$$

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}.

$$11x^{1-1}+7\left(-202\right)x^{7-1}$$

Subtract 1 from 1.

$$11x^{0}+7\left(-202\right)x^{7-1}$$

Multiply 7 times -202.

$$11x^{0}-1414x^{7-1}$$

Subtract 1 from 7.

$$11x^{0}-1414x^{6}$$

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

$$11\times 1-1414x^{6}$$

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

$$11-1414x^{6}$$

Evaluate

$$1+11x-202x^{7}$$

Solution Steps

Combine x and 10x to get 11x.

$$11x-202x^{7}+1$$