Solve 1/2a*3/4adiv2

$$\frac { 1 } { 2 } a \times \frac { 3 } { 4 } a \div 2$$

Evaluate

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

Solution Steps

Multiply a and a to get a^{2}.

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

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

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

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{\frac{3}{8}a^{2}}{2}$$

Divide \frac{3}{8}a^{2} by 2 to get \frac{3}{16}a^{2}.

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

Differentiate w.r.t. a

$$\frac{3a}{8}$$

Steps Using Definition of a Derivative

Multiply a and a to get a^{2}.

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

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

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

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{3}{8}a^{2}}{2})$$

Divide \frac{3}{8}a^{2} by 2 to get \frac{3}{16}a^{2}.

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

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

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

Multiply 2 times \frac{3}{16}.

$$\frac{3}{8}a^{2-1}$$

Subtract 1 from 2.

$$\frac{3}{8}a^{1}$$

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

$$\frac{3}{8}a$$