Solve x^4-3-3x^2+2x-6

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Subtract 6 from -3 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-9-3x^{2}+2x)$$

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}.

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

Subtract 1 from 4.

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

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.

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

Evaluate

$$x^{4}-3x^{2}+2x-9$$

Solution Steps

Subtract 6 from -3 to get -9.

$$x^{4}-9-3x^{2}+2x$$