Solve 3/5x-2/3x+1/4x

$$\frac { 3 } { 5 } x - \frac { 2 } { 3 } x + \frac { 1 } { 4 } x$$

Evaluate

$$\frac{11x}{60}$$

Solution Steps

Combine \frac{3}{5}x and -\frac{2}{3}x to get -\frac{1}{15}x.

$$-\frac{1}{15}x+\frac{1}{4}x$$

Combine -\frac{1}{15}x and \frac{1}{4}x to get \frac{11}{60}x.

$$\frac{11}{60}x$$

Differentiate w.r.t. x

$$\frac{11}{60} = 0.18333333333333332$$

Steps Using Definition of a Derivative

Combine \frac{3}{5}x and -\frac{2}{3}x to get -\frac{1}{15}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{15}x+\frac{1}{4}x)$$

Combine -\frac{1}{15}x and \frac{1}{4}x to get \frac{11}{60}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11}{60}x)$$

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

$$\frac{11}{60}x^{1-1}$$

Subtract 1 from 1.

$$\frac{11}{60}x^{0}$$

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

$$\frac{11}{60}\times 1$$

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

$$\frac{11}{60}$$