Solve x^4+7x^3+7x^2+15

$${ x }^{ 4 } +7 { x }^{ 3 } +7 { x }^{ 2 } +15$$

Differentiate w.r.t. x

$$x\left(4x^{2}+21x+14\right)$$

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}.

$$4x^{4-1}+3\times 7x^{3-1}+2\times 7x^{2-1}$$

Subtract 1 from 4.

$$4x^{3}+3\times 7x^{3-1}+2\times 7x^{2-1}$$

Multiply 3 times 7.

$$4x^{3}+21x^{3-1}+2\times 7x^{2-1}$$

Subtract 1 from 3.

$$4x^{3}+21x^{2}+2\times 7x^{2-1}$$

Multiply 3 times 7.

$$4x^{3}+21x^{2}+14x^{2-1}$$

Subtract 1 from 2.

$$4x^{3}+21x^{2}+14x^{1}$$

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

$$4x^{3}+21x^{2}+14x$$

Evaluate

$$x^{4}+7x^{3}+7x^{2}+15$$