Solve 4a^2/3*a/16a

$$\frac { 4 a ^ { 2 } } { 3 } \times \frac { a } { 16 a }$$

Evaluate

$$\frac{a^{2}}{12}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$\frac{4a^{2}}{3}\times \frac{1}{16}$$

Multiply \frac{4a^{2}}{3} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4a^{2}}{3\times 16}$$

Cancel out 4 in both numerator and denominator.

$$\frac{a^{2}}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{a^{2}}{12}$$

Differentiate w.r.t. a

$$\frac{a}{6}$$

Steps Using Definition of a Derivative

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4a^{2}}{3}\times \frac{1}{16})$$

Multiply \frac{4a^{2}}{3} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4a^{2}}{3\times 16})$$

Cancel out 4 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{3\times 4})$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{12})$$

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

$$2\times \frac{1}{12}a^{2-1}$$

Multiply 2 times \frac{1}{12}.

$$\frac{1}{6}a^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{6}a^{1}$$

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

$$\frac{1}{6}a$$