Solve (-3/x)(23/3x^3)

$$(- \frac{ 3 }{ x } )( \frac{ 23 }{ 3 } { x }^{ 3 } )$$

Evaluate

$$-23x^{2}$$

Solution Steps

Multiply -\frac{3}{x} times \frac{23}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 23}{x\times 3}x^{3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-23}{x}x^{3}$$

Express \frac{-23}{x}x^{3} as a single fraction.

$$\frac{-23x^{3}}{x}$$

Cancel out x in both numerator and denominator.

$$-23x^{2}$$

Differentiate w.r.t. x

$$-46x$$

Steps Using Definition of a Derivative

Multiply -\frac{3}{x} times \frac{23}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3\times 23}{x\times 3}x^{3})$$

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-23}{x}x^{3})$$

Express \frac{-23}{x}x^{3} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-23x^{3}}{x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-23x^{2})$$

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

$$2\left(-23\right)x^{2-1}$$

Multiply 2 times -23.

$$-46x^{2-1}$$

Subtract 1 from 2.

$$-46x^{1}$$

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

$$-46x$$