Solve (-4-2x)+(-4x^2-2x+5x^3)

$$( - 4 - 2 x ) + ( - 4 x ^ { 2 } - 2 x + 5 x ^ { 3 } )$$

Differentiate w.r.t. x

$$15x^{2}-8x-4$$

Steps Using Derivative Rule for Sum

Combine -2x and -2x to get -4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4-4x-4x^{2}+5x^{3})$$

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}.

$$-4x^{1-1}+2\left(-4\right)x^{2-1}+3\times 5x^{3-1}$$

Subtract 1 from 1.

$$-4x^{0}+2\left(-4\right)x^{2-1}+3\times 5x^{3-1}$$

Multiply 2 times -4.

$$-4x^{0}-8x^{2-1}+3\times 5x^{3-1}$$

Subtract 1 from 2.

$$-4x^{0}-8x^{1}+3\times 5x^{3-1}$$

Multiply 2 times -4.

$$-4x^{0}-8x^{1}+15x^{3-1}$$

Subtract 1 from 3.

$$-4x^{0}-8x^{1}+15x^{2}$$

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

$$-4x^{0}-8x+15x^{2}$$

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

$$-4-8x+15x^{2}$$

Evaluate

$$5x^{3}-4x^{2}-4x-4$$

Solution Steps

Combine -2x and -2x to get -4x.

$$-4-4x-4x^{2}+5x^{3}$$