Solve a3/4:a^frac{1{4}}

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

Differentiate w.r.t. a

$$\frac{9}{16\sqrt[4]{a}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Do the arithmetic.

$$\frac{9}{16}a^{-\frac{1}{4}}$$

Evaluate

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

Solution Steps

Cancel out \sqrt[4]{a} in both numerator and denominator.

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