Solve x^4-8x^2-9left|0.3right|

$${ x }^{ 4 } -8 { x }^{ 2 } -9 \left| 0.3 \right|$$

Evaluate

$$x^{4}-8x^{2}-2.7$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0.3 is 0.3.

$$x^{4}-8x^{2}-9\times 0.3$$

Multiply 9 and 0.3 to get 2.7.

$$x^{4}-8x^{2}-2.7$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0.3 is 0.3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-8x^{2}-9\times 0.3)$$

Multiply 9 and 0.3 to get 2.7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-8x^{2}-2.7)$$

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}.

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

Subtract 1 from 4.

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

Multiply 2 times -8.

$$4x^{3}-16x^{2-1}$$

Subtract 1 from 2.

$$4x^{3}-16x^{1}$$

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

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