Solve -x^{2}+1/2x^{2})(-a-1/4a);quad(a^{4}-4a^4)(a^2-3a^2+a^2)

$$- x ^ { 2 } + \frac { 1 } { 2 } x ^ { 2 } ) ( - a - \frac { 1 } { 4 } a ) ; \quad ( a ^ { 4 } - 4 a ^ { 4 } ) ( a ^ { 2 } - 3 a ^ { 2 } + a ^ { 2 } )$$

Differentiate w.r.t. x

$$-x$$

Steps Using Definition of a Derivative

Combine -x^{2} and \frac{1}{2}x^{2} to get -\frac{1}{2}x^{2}.

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

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

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

Multiply 2 times -\frac{1}{2}.

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

Subtract 1 from 2.

$$-x^{1}$$

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

$$-x$$

Evaluate

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

Solution Steps

Combine -x^{2} and \frac{1}{2}x^{2} to get -\frac{1}{2}x^{2}.

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