Solve (5n^2)+(-1/3n^2)+(-1/2n^2)

$$( 5 n ^ { 2 } ) + ( - \frac { 1 } { 3 } n ^ { 2 } ) + ( - \frac { 1 } { 2 } n ^ { 2 } )$$

Evaluate

$$\frac{25n^{2}}{6}$$

Solution Steps

Combine 5n^{2} and -\frac{1}{3}n^{2} to get \frac{14}{3}n^{2}.

$$\frac{14}{3}n^{2}-\frac{1}{2}n^{2}$$

Combine \frac{14}{3}n^{2} and -\frac{1}{2}n^{2} to get \frac{25}{6}n^{2}.

$$\frac{25}{6}n^{2}$$

Differentiate w.r.t. n

$$\frac{25n}{3}$$

Steps Using Definition of a Derivative

Combine 5n^{2} and -\frac{1}{3}n^{2} to get \frac{14}{3}n^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{14}{3}n^{2}-\frac{1}{2}n^{2})$$

Combine \frac{14}{3}n^{2} and -\frac{1}{2}n^{2} to get \frac{25}{6}n^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{25}{6}n^{2})$$

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

$$2\times \frac{25}{6}n^{2-1}$$

Multiply 2 times \frac{25}{6}.

$$\frac{25}{3}n^{2-1}$$

Subtract 1 from 2.

$$\frac{25}{3}n^{1}$$

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

$$\frac{25}{3}n$$