Solve x-8div4x^3-15^2-120x-128

$$x-8 \div 4 { x }^{ 3 } - { 15 }^{ 2 } -120x-128$$

Evaluate

$$-2x^{3}-119x-353$$

Solution Steps

Divide 8 by 4 to get 2.

$$x-2x^{3}-15^{2}-120x-128$$

Calculate 15 to the power of 2 and get 225.

$$x-2x^{3}-225-120x-128$$

Combine x and -120x to get -119x.

$$-119x-2x^{3}-225-128$$

Subtract 128 from -225 to get -353.

$$-119x-2x^{3}-353$$

Differentiate w.r.t. x

$$-6x^{2}-119$$

Steps Using Derivative Rule for Sum

Divide 8 by 4 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-2x^{3}-15^{2}-120x-128)$$

Calculate 15 to the power of 2 and get 225.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-2x^{3}-225-120x-128)$$

Combine x and -120x to get -119x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-119x-2x^{3}-225-128)$$

Subtract 128 from -225 to get -353.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-119x-2x^{3}-353)$$

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}.

$$-119x^{1-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 1.

$$-119x^{0}+3\left(-2\right)x^{3-1}$$

Multiply 3 times -2.

$$-119x^{0}-6x^{3-1}$$

Subtract 1 from 3.

$$-119x^{0}-6x^{2}$$

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

$$-119-6x^{2}$$