Solve a-1/3a*3/4

$$a - \frac { 1 } { 3 } a \times \frac { 3 } { 4 }$$

Evaluate

$$\frac{3a}{4}$$

Solution Steps

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

$$a-\frac{1\times 3}{3\times 4}a$$

Cancel out 3 in both numerator and denominator.

$$a-\frac{1}{4}a$$

Combine a and -\frac{1}{4}a to get \frac{3}{4}a.

$$\frac{3}{4}a$$

Differentiate w.r.t. a

$$\frac{3}{4} = 0.75$$

Steps Using Definition of a Derivative

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

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

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a-\frac{1}{4}a)$$

Combine a and -\frac{1}{4}a to get \frac{3}{4}a.

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

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

$$\frac{3}{4}a^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{4}a^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{3}{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{3}{4}$$