Solve d/dx(x^3+x^2/x-2x)

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

Evaluate

$$-2x-1$$

Steps Using Derivative Rule for Sum

Combine x and -2x to get -x.

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

Factor the expressions that are not already factored in \frac{x^{3}+x^{2}}{-x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x+1\right)x^{2}}{-x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+1\right)}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x\left(x+1\right))$$

Use the distributive property to multiply x by x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(x^{2}+x\right))$$

To find the opposite of x^{2}+x, find the opposite of each term.

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

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}.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$-2x^{1}-x^{0}$$

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

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

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

$$-2x-1$$

Differentiate w.r.t. x

$$-2$$