Solve (4x^3)*2/x

$$( 4 x ^ { 3 } ) \times \frac { 2 } { x }$$

Evaluate

$$8x^{2}$$

Solution Steps

Express 4\times \frac{2}{x} as a single fraction.

$$\frac{4\times 2}{x}x^{3}$$

Multiply 4 and 2 to get 8.

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

Express \frac{8}{x}x^{3} as a single fraction.

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

Cancel out x in both numerator and denominator.

$$8x^{2}$$

Differentiate w.r.t. x

$$16x$$

Steps Using Definition of a Derivative

Express 4\times \frac{2}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 2}{x}x^{3})$$

Multiply 4 and 2 to get 8.

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

Express \frac{8}{x}x^{3} as a single fraction.

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

Cancel out x in both numerator and denominator.

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

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

$$2\times 8x^{2-1}$$

Multiply 2 times 8.

$$16x^{2-1}$$

Subtract 1 from 2.

$$16x^{1}$$

For any term t, t^{1}=t.

$$16x$$