Solve x^3+40x^2-42x-35

$$x ^ { 3 } + 40 x ^ { 2 } - 42 x - 35$$

Differentiate w.r.t. x

$$3x^{2}+80x-42$$

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}.

$$3x^{3-1}+2\times 40x^{2-1}-42x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 40x^{2-1}-42x^{1-1}$$

Multiply 2 times 40.

$$3x^{2}+80x^{2-1}-42x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}+80x^{1}-42x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}+80x^{1}-42x^{0}$$

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

$$3x^{2}+80x-42x^{0}$$

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

$$3x^{2}+80x-42$$

Evaluate

$$x^{3}+40x^{2}-42x-35$$