Solve x^6+6x^4-12x^2+8

$$x ^ { 6 } + 6 x ^ { 4 } - 12 x ^ { 2 } + 8$$

Differentiate w.r.t. x

$$6x\left(x^{4}+4x^{2}-4\right)$$

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}.

$$6x^{6-1}+4\times 6x^{4-1}+2\left(-12\right)x^{2-1}$$

Subtract 1 from 6.

$$6x^{5}+4\times 6x^{4-1}+2\left(-12\right)x^{2-1}$$

Multiply 4 times 6.

$$6x^{5}+24x^{4-1}+2\left(-12\right)x^{2-1}$$

Subtract 1 from 4.

$$6x^{5}+24x^{3}+2\left(-12\right)x^{2-1}$$

Multiply 4 times 6.

$$6x^{5}+24x^{3}-24x^{2-1}$$

Subtract 1 from 2.

$$6x^{5}+24x^{3}-24x^{1}$$

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

$$6x^{5}+24x^{3}-24x$$

Evaluate

$$x^{6}+6x^{4}-12x^{2}+8$$