Solve (-2/3w^2)+(-w^2)*(-2/10)

$$( - \frac { 2 } { 3 } w ^ { 2 } ) + ( - w ^ { 2 } ) \times ( - \frac { 2 } { 10 } )$$

Evaluate

$$-\frac{7w^{2}}{15}$$

Solution Steps

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}w^{2}+\left(-w^{2}\right)\left(-\frac{1}{5}\right)$$

Multiply -1 and -\frac{1}{5} to get \frac{1}{5}.

$$-\frac{2}{3}w^{2}+\frac{1}{5}w^{2}$$

Combine -\frac{2}{3}w^{2} and \frac{1}{5}w^{2} to get -\frac{7}{15}w^{2}.

$$-\frac{7}{15}w^{2}$$

Differentiate w.r.t. w

$$-\frac{14w}{15}$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-\frac{2}{3}w^{2}+\left(-w^{2}\right)\left(-\frac{1}{5}\right))$$

Multiply -1 and -\frac{1}{5} to get \frac{1}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-\frac{2}{3}w^{2}+\frac{1}{5}w^{2})$$

Combine -\frac{2}{3}w^{2} and \frac{1}{5}w^{2} to get -\frac{7}{15}w^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-\frac{7}{15}w^{2})$$

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

$$2\left(-\frac{7}{15}\right)w^{2-1}$$

Multiply 2 times -\frac{7}{15}.

$$-\frac{14}{15}w^{2-1}$$

Subtract 1 from 2.

$$-\frac{14}{15}w^{1}$$

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

$$-\frac{14}{15}w$$