Solve P(x)=2x^4-x^3+2x^2-6

$$P ( x ) = 2 x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 6$$

Differentiate w.r.t. x

$$x\left(8x^{2}-3x+4\right)$$

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}.

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

Multiply 4 times 2.

$$8x^{4-1}+3\left(-1\right)x^{3-1}+2\times 2x^{2-1}$$

Subtract 1 from 4.

$$8x^{3}+3\left(-1\right)x^{3-1}+2\times 2x^{2-1}$$

Multiply 3 times -1.

$$8x^{3}-3x^{3-1}+2\times 2x^{2-1}$$

Subtract 1 from 3.

$$8x^{3}-3x^{2}+2\times 2x^{2-1}$$

Multiply 3 times -1.

$$8x^{3}-3x^{2}+4x^{2-1}$$

Subtract 1 from 2.

$$8x^{3}-3x^{2}+4x^{1}$$

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

$$8x^{3}-3x^{2}+4x$$

Evaluate

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