Solve 51x^4+3x^2+x+2

$$51 x ^ { 4 } + 3 x ^ { 2 } + x + 2$$

Differentiate w.r.t. x

$$204x^{3}+6x+1$$

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}.

$$4\times 51x^{4-1}+2\times 3x^{2-1}+x^{1-1}$$

Multiply 4 times 51.

$$204x^{4-1}+2\times 3x^{2-1}+x^{1-1}$$

Subtract 1 from 4.

$$204x^{3}+2\times 3x^{2-1}+x^{1-1}$$

Multiply 2 times 3.

$$204x^{3}+6x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$204x^{3}+6x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$204x^{3}+6x^{1}+x^{0}$$

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

$$204x^{3}+6x+x^{0}$$

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

$$204x^{3}+6x+1$$

Evaluate

$$51x^{4}+3x^{2}+x+2$$