Solve 5/6(-7x)

$$\frac { 5 } { 6 } ( - 7 x )$$

Evaluate

$$-\frac{35x}{6}$$

Solution Steps

Express \frac{5}{6}\left(-7\right) as a single fraction.

$$\frac{5\left(-7\right)}{6}x$$

Multiply 5 and -7 to get -35.

$$\frac{-35}{6}x$$

Fraction \frac{-35}{6} can be rewritten as -\frac{35}{6} by extracting the negative sign.

$$-\frac{35}{6}x$$

Differentiate w.r.t. x

$$-\frac{35}{6} = -5\frac{5}{6} = -5.833333333333333$$

Steps Using Definition of a Derivative

Express \frac{5}{6}\left(-7\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(-7\right)}{6}x)$$

Multiply 5 and -7 to get -35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-35}{6}x)$$

Fraction \frac{-35}{6} can be rewritten as -\frac{35}{6} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{35}{6}x)$$

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

$$-\frac{35}{6}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{35}{6}x^{0}$$

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

$$-\frac{35}{6}$$