Solve x^2-4x^8-5x^2+x+8

$${ x }^{ 2 } -4 { x }^{ 8 } -5 { x }^{ 2 } +x+8$$

Differentiate w.r.t. x

$$1-8x-32x^{7}$$

Steps Using Derivative Rule for Sum

Combine x^{2} and -5x^{2} to get -4x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{2}-4x^{8}+x+8)$$

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}.

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

Multiply 2 times -4.

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

Subtract 1 from 2.

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

Multiply 8 times -4.

$$-8x^{1}-32x^{8-1}+x^{1-1}$$

Subtract 1 from 8.

$$-8x^{1}-32x^{7}+x^{1-1}$$

Subtract 1 from 1.

$$-8x^{1}-32x^{7}+x^{0}$$

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

$$-8x-32x^{7}+x^{0}$$

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

$$-8x-32x^{7}+1$$

Evaluate

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

Solution Steps

Combine x^{2} and -5x^{2} to get -4x^{2}.

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