Solve 4x^4/3*5x^1/2

$$4 x ^ { 4 / 3 } \cdot 5 x ^ { 1 / 2 }$$

Evaluate

$$20x^{\frac{11}{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{4}{3} and \frac{1}{2} to get \frac{11}{6}.

$$4x^{\frac{11}{6}}\times 5$$

Multiply 4 and 5 to get 20.

$$20x^{\frac{11}{6}}$$

Differentiate w.r.t. x

$$\frac{110x^{\frac{5}{6}}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{4}{3} and \frac{1}{2} to get \frac{11}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{\frac{11}{6}}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{\frac{11}{6}})$$

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

$$\frac{11}{6}\times 20x^{\frac{11}{6}-1}$$

Multiply \frac{11}{6} times 20.

$$\frac{110}{3}x^{\frac{11}{6}-1}$$

Subtract 1 from \frac{11}{6}.

$$\frac{110}{3}x^{\frac{5}{6}}$$