Solve 9x-5x^4+8x^2+4x^4+8-12x-3x

$$9 x - 5 x ^ { 4 } + 8 x ^ { 2 } + 4 x ^ { 4 } + 8 - 12 x - 3 x$$

Evaluate

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

Solution Steps

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

$$9x-x^{4}+8x^{2}+8-12x-3x$$

Combine 9x and -12x to get -3x.

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

Combine -3x and -3x to get -6x.

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

Differentiate w.r.t. x

$$-4x^{3}+16x-6$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-x^{4}+8x^{2}+8-12x-3x)$$

Combine 9x and -12x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x-x^{4}+8x^{2}+8-3x)$$

Combine -3x and -3x to get -6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x-x^{4}+8x^{2}+8)$$

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}.

$$-6x^{1-1}+4\left(-1\right)x^{4-1}+2\times 8x^{2-1}$$

Subtract 1 from 1.

$$-6x^{0}+4\left(-1\right)x^{4-1}+2\times 8x^{2-1}$$

Multiply 4 times -1.

$$-6x^{0}-4x^{4-1}+2\times 8x^{2-1}$$

Subtract 1 from 4.

$$-6x^{0}-4x^{3}+2\times 8x^{2-1}$$

Multiply 4 times -1.

$$-6x^{0}-4x^{3}+16x^{2-1}$$

Subtract 1 from 2.

$$-6x^{0}-4x^{3}+16x^{1}$$

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

$$-6x^{0}-4x^{3}+16x$$

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

$$-6-4x^{3}+16x$$