Solve 5a^2/4+5a^2/16

$$\frac { 5 a ^ { 2 } } { 4 } + \frac { 5 a ^ { 2 } } { 16 }$$

Evaluate

$$\frac{25a^{2}}{16}$$

Solution Steps

Combine \frac{5a^{2}}{4} and \frac{5a^{2}}{16} to get \frac{5}{16}\times 5a^{2}.

$$\frac{5}{16}\times 5a^{2}$$

Multiply \frac{5}{16} and 5 to get \frac{25}{16}.

$$\frac{25}{16}a^{2}$$

Differentiate w.r.t. a

$$\frac{25a}{8}$$

Steps Using Definition of a Derivative

Combine \frac{5a^{2}}{4} and \frac{5a^{2}}{16} to get \frac{5}{16}\times 5a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{16}\times 5a^{2})$$

Multiply \frac{5}{16} and 5 to get \frac{25}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{25}{16}a^{2})$$

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

$$2\times \frac{25}{16}a^{2-1}$$

Multiply 2 times \frac{25}{16}.

$$\frac{25}{8}a^{2-1}$$

Subtract 1 from 2.

$$\frac{25}{8}a^{1}$$

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

$$\frac{25}{8}a$$