Solve -x^4(2xyz^2)^0/x^2

$$\frac { - x ^ { 4 } ( 2 x y z ^ { 2 } ) ^ { 0 } } { x ^ { 2 } }$$

Evaluate

$$-x^{2}$$

Short Solution Steps

Calculate 2xyz^{2} to the power of 0 and get 1.

$$\frac{\left(-x^{4}\right)\times 1}{x^{2}}$$

Factor the expressions that are not already factored.

$$\frac{-x^{4}}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$-x^{2}$$

Differentiate w.r.t. x

$$-2x$$

Steps Using Definition of a Derivative

Calculate 2xyz^{2} to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-x^{4}\right)\times 1}{x^{2}})$$

Factor the expressions that are not already factored in \frac{\left(-x^{4}\right)\times 1}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

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

The derivative of ax^{n} is nax^{n-1}.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$