Solve a^2+1/4a^2

$$a ^ { 2 } + \frac { 1 } { 4 } a ^ { 2 }$$

Differentiate w.r.t. a

$$\frac{5a}{2}$$

Steps Using Definition of a Derivative

Combine a^{2} and \frac{1}{4}a^{2} to get \frac{5}{4}a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{4}a^{2})$$

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

$$2\times \frac{5}{4}a^{2-1}$$

Multiply 2 times \frac{5}{4}.

$$\frac{5}{2}a^{2-1}$$

Subtract 1 from 2.

$$\frac{5}{2}a^{1}$$

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

$$\frac{5}{2}a$$

Evaluate

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

Solution Steps

Combine a^{2} and \frac{1}{4}a^{2} to get \frac{5}{4}a^{2}.

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