Solve 3x^4-4x^3-3x-1

$$3 x ^ { 4 } - 4 x ^ { 3 } - 3 x - 1$$

Differentiate w.r.t. x

$$12x^{3}-12x^{2}-3$$

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}.

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

Multiply 4 times 3.

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

Subtract 1 from 4.

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

Multiply 3 times -4.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

$$12x^{3}-12x^{2}-3x^{0}$$

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

$$12x^{3}-12x^{2}-3$$

Evaluate

$$3x^{4}-4x^{3}-3x-1$$