Solve 4x^3div6x^2

$$4 x ^ { 3 } \div 6 x ^ { 2 }$$

Evaluate

$$\frac{2x^{5}}{3}$$

Solution Steps

Divide 4x^{3} by 6 to get \frac{2}{3}x^{3}.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{2}{3}x^{5}$$

Differentiate w.r.t. x

$$\frac{10x^{4}}{3}$$

Steps Using Definition of a Derivative

Divide 4x^{3} by 6 to get \frac{2}{3}x^{3}.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}x^{5})$$

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

$$5\times \frac{2}{3}x^{5-1}$$

Multiply 5 times \frac{2}{3}.

$$\frac{10}{3}x^{5-1}$$

Subtract 1 from 5.

$$\frac{10}{3}x^{4}$$