Solve frac{a^frac{2{3}}}{7^3}

$$\frac { a ^ { \frac { 2 } { 3 } } } { 7 ^ { 3 } }$$

Differentiate w.r.t. a

$$\frac{2}{1029\sqrt[3]{a}}$$

Steps Using Definition of a Derivative

Calculate 7 to the power of 3 and get 343.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{\frac{2}{3}}}{343})$$

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

$$\frac{2}{3}\times \frac{1}{343}a^{\frac{2}{3}-1}$$

Multiply \frac{2}{3} times \frac{1}{343} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{2}{1029}a^{\frac{2}{3}-1}$$

Subtract 1 from \frac{2}{3}.

$$\frac{2}{1029}a^{-\frac{1}{3}}$$

Evaluate

$$\frac{a^{\frac{2}{3}}}{343}$$