Solve 8x^2*4/x

$$8 { x }^{ 2 } \times \frac{ 4 }{ x }$$

Evaluate

$$32x$$

Solution Steps

Express 8\times \frac{4}{x} as a single fraction.

$$\frac{8\times 4}{x}x^{2}$$

Multiply 8 and 4 to get 32.

$$\frac{32}{x}x^{2}$$

Express \frac{32}{x}x^{2} as a single fraction.

$$\frac{32x^{2}}{x}$$

Cancel out x in both numerator and denominator.

$$32x$$

Differentiate w.r.t. x

$$32$$

Steps Using Definition of a Derivative

Express 8\times \frac{4}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8\times 4}{x}x^{2})$$

Multiply 8 and 4 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32}{x}x^{2})$$

Express \frac{32}{x}x^{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32x^{2}}{x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x)$$

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

$$32x^{1-1}$$

Subtract 1 from 1.

$$32x^{0}$$

For any term t except 0, t^{0}=1.

$$32\times 1$$

For any term t, t\times 1=t and 1t=t.

$$32$$