Solve (1/15)(-10x)(-6)

$$( \frac { 1 } { 15 } ) ( - 10 x ) ( - 6 )$$

Evaluate

$$4x$$

Solution Steps

Multiply \frac{1}{15} and -10 to get \frac{-10}{15}.

$$\frac{-10}{15}x\left(-6\right)$$

Reduce the fraction \frac{-10}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{2}{3}x\left(-6\right)$$

Express -\frac{2}{3}\left(-6\right) as a single fraction.

$$\frac{-2\left(-6\right)}{3}x$$

Multiply -2 and -6 to get 12.

$$\frac{12}{3}x$$

Divide 12 by 3 to get 4.

$$4x$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Multiply \frac{1}{15} and -10 to get \frac{-10}{15}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-10}{15}x\left(-6\right))$$

Reduce the fraction \frac{-10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{3}x\left(-6\right))$$

Express -\frac{2}{3}\left(-6\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2\left(-6\right)}{3}x)$$

Multiply -2 and -6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{3}x)$$

Divide 12 by 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x)$$

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

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

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

$$4\times 1$$

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

$$4$$