Solve (x^4+3x^2+2x)^prime

$$( x ^ { 4 } + 3 x ^ { 2 } + 2 x ) ^ { \prime }$$

Evaluate

$$4x^{3}+6x+2$$

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}.

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

Subtract 1 from 4.

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

Multiply 2 times 3.

$$4x^{3}+6x^{2-1}+2x^{1-1}$$

Subtract 1 from 2.

$$4x^{3}+6x^{1}+2x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}+6x^{1}+2x^{0}$$

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

$$4x^{3}+6x+2x^{0}$$

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

$$4x^{3}+6x+2\times 1$$

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

$$4x^{3}+6x+2$$

Differentiate w.r.t. x

$$12x^{2}+6$$