Solve (3x^5/6)(8x^2/3)=

$$( 3 x ^ { 5 / 6 } ) ( 8 x ^ { 2 / 3 } ) =$$

Evaluate

$$24x^{\frac{3}{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{5}{6} and \frac{2}{3} to get \frac{3}{2}.

$$3x^{\frac{3}{2}}\times 8$$

Multiply 3 and 8 to get 24.

$$24x^{\frac{3}{2}}$$

Differentiate w.r.t. x

$$36\sqrt{x}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{5}{6} and \frac{2}{3} to get \frac{3}{2}.

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

Multiply 3 and 8 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{\frac{3}{2}})$$

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

$$\frac{3}{2}\times 24x^{\frac{3}{2}-1}$$

Multiply \frac{3}{2} times 24.

$$36x^{\frac{3}{2}-1}$$

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

$$36\sqrt{x}$$