Solve f(x)=-2/3x*5

$$f ( x ) = - \frac { 2 } { 3 } x \cdot 5$$

Evaluate

$$-\frac{10x}{3}$$

Solution Steps

Express -\frac{2}{3}\times 5 as a single fraction.

$$\frac{-2\times 5}{3}x$$

Multiply -2 and 5 to get -10.

$$\frac{-10}{3}x$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$-\frac{10}{3}x$$

Differentiate w.r.t. x

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$

Steps Using Definition of a Derivative

Express -\frac{2}{3}\times 5 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2\times 5}{3}x)$$

Multiply -2 and 5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-10}{3}x)$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{10}{3}x)$$

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

$$-\frac{10}{3}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{10}{3}x^{0}$$

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

$$-\frac{10}{3}$$