Solve x^3+5x^2+x+6)=0

$$x ^ { 3 } + 5 x ^ { 2 } + x + 6 ) = 0$$

Differentiate w.r.t. x

$$3x^{2}+10x+1$$

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}.

$$3x^{3-1}+2\times 5x^{2-1}+x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 5x^{2-1}+x^{1-1}$$

Multiply 2 times 5.

$$3x^{2}+10x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}+10x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}+10x^{1}+x^{0}$$

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

$$3x^{2}+10x+x^{0}$$

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

$$3x^{2}+10x+1$$

Evaluate

$$x^{3}+5x^{2}+x+6$$