Solve 3x^3+2x^2+5x-6

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

Differentiate w.r.t. x

$$9x^{2}+4x+5$$

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+2\times 2x^{2-1}+5x^{1-1}$$

Subtract 1 from 3.

$$9x^{2}+2\times 2x^{2-1}+5x^{1-1}$$

Multiply 2 times 2.

$$9x^{2}+4x^{2-1}+5x^{1-1}$$

Subtract 1 from 2.

$$9x^{2}+4x^{1}+5x^{1-1}$$

Subtract 1 from 1.

$$9x^{2}+4x^{1}+5x^{0}$$

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

$$9x^{2}+4x+5x^{0}$$

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

$$9x^{2}+4x+5\times 1$$

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

$$9x^{2}+4x+5$$

Evaluate

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