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

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

Evaluate

$$20x^{\frac{11}{3}}$$

Solution Steps

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

$$4x^{\frac{11}{3}}\times 5$$

Multiply 4 and 5 to get 20.

$$20x^{\frac{11}{3}}$$

Differentiate w.r.t. x

$$\frac{220x^{\frac{8}{3}}}{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{\frac{11}{3}}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{\frac{11}{3}})$$

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

$$\frac{11}{3}\times 20x^{\frac{11}{3}-1}$$

Multiply \frac{11}{3} times 20.

$$\frac{220}{3}x^{\frac{11}{3}-1}$$

Subtract 1 from \frac{11}{3}.

$$\frac{220}{3}x^{\frac{8}{3}}$$