Solve =3x^4-4x^2+x-2

$$= 3 x ^ { 4 } - 4 x ^ { 2 } + x - 2$$

Differentiate w.r.t. x

$$12x^{3}-8x+1$$

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}.

$$4\times 3x^{4-1}+2\left(-4\right)x^{2-1}+x^{1-1}$$

Multiply 4 times 3.

$$12x^{4-1}+2\left(-4\right)x^{2-1}+x^{1-1}$$

Subtract 1 from 4.

$$12x^{3}+2\left(-4\right)x^{2-1}+x^{1-1}$$

Multiply 2 times -4.

$$12x^{3}-8x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$12x^{3}-8x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$12x^{3}-8x^{1}+x^{0}$$

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

$$12x^{3}-8x+x^{0}$$

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

$$12x^{3}-8x+1$$

Evaluate

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