Solve 2x^3+9x^2+54x+27

$$2 { x }^{ 3 } +9 { x }^{ 2 } +54x+27$$

Differentiate w.r.t. x

$$6\left(x^{2}+3x+9\right)$$

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}.

$$3\times 2x^{3-1}+2\times 9x^{2-1}+54x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\times 9x^{2-1}+54x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+2\times 9x^{2-1}+54x^{1-1}$$

Multiply 2 times 9.

$$6x^{2}+18x^{2-1}+54x^{1-1}$$

Subtract 1 from 2.

$$6x^{2}+18x^{1}+54x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}+18x^{1}+54x^{0}$$

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

$$6x^{2}+18x+54x^{0}$$

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

$$6x^{2}+18x+54\times 1$$

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

$$6x^{2}+18x+54$$

Evaluate

$$2x^{3}+9x^{2}+54x+27$$