Solve (3x^516)(8x^2/3)

$$( 3 x ^ { 5 } 16 ) ( 8 x ^ { 2 / 3 } )$$

Evaluate

$$384x^{\frac{17}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and \frac{2}{3} to get \frac{17}{3}.

$$3x^{\frac{17}{3}}\times 16\times 8$$

Multiply 3 and 16 to get 48.

$$48x^{\frac{17}{3}}\times 8$$

Multiply 48 and 8 to get 384.

$$384x^{\frac{17}{3}}$$

Differentiate w.r.t. x

$$2176x^{\frac{14}{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and \frac{2}{3} to get \frac{17}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{\frac{17}{3}}\times 16\times 8)$$

Multiply 3 and 16 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}x}(48x^{\frac{17}{3}}\times 8)$$

Multiply 48 and 8 to get 384.

$$\frac{\mathrm{d}}{\mathrm{d}x}(384x^{\frac{17}{3}})$$

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

$$\frac{17}{3}\times 384x^{\frac{17}{3}-1}$$

Multiply \frac{17}{3} times 384.

$$2176x^{\frac{17}{3}-1}$$

Subtract 1 from \frac{17}{3}.

$$2176x^{\frac{14}{3}}$$