Solve -4x+5x^3-4x^3+3x-5

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

Evaluate

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

Solution Steps

Combine 5x^{3} and -4x^{3} to get x^{3}.

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

Combine -4x and 3x to get -x.

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Combine 5x^{3} and -4x^{3} to get x^{3}.

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

Combine -4x and 3x to get -x.

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

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}.

$$-x^{1-1}+3x^{3-1}$$

Subtract 1 from 1.

$$-x^{0}+3x^{3-1}$$

Subtract 1 from 3.

$$-x^{0}+3x^{2}$$

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

$$-1+3x^{2}$$