Solve a^3/2(4a^2/3)

$$a ^ { 3 / 2 } ( 4 a ^ { 2 / 3 } )$$

Differentiate w.r.t. a

$$\frac{26a^{\frac{7}{6}}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{2}{3} to get \frac{13}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{13}{6}}\times 4)$$

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

$$\frac{13}{6}\times 4a^{\frac{13}{6}-1}$$

Multiply \frac{13}{6} times 4.

$$\frac{26}{3}a^{\frac{13}{6}-1}$$

Subtract 1 from \frac{13}{6}.

$$\frac{26}{3}a^{\frac{7}{6}}$$

Evaluate

$$4a^{\frac{13}{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{2}{3} to get \frac{13}{6}.

$$a^{\frac{13}{6}}\times 4$$