Solve x/3+5x/9-5x/18

$$\frac { x } { 3 } + \frac { 5 x } { 9 } - \frac { 5 x } { 18 }$$

Evaluate

$$\frac{11x}{18}$$

Solution Steps

Combine \frac{5x}{9} and -\frac{5x}{18} to get \frac{1}{18}\times 5x.

$$\frac{x}{3}+\frac{1}{18}\times 5x$$

Multiply \frac{1}{18} and 5 to get \frac{5}{18}.

$$\frac{x}{3}+\frac{5}{18}x$$

Combine \frac{x}{3} and \frac{5}{18}x to get \frac{11}{18}x.

$$\frac{11}{18}x$$

Differentiate w.r.t. x

$$\frac{11}{18} = 0.6111111111111112$$

Steps Using Definition of a Derivative

Combine \frac{5x}{9} and -\frac{5x}{18} to get \frac{1}{18}\times 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{3}+\frac{1}{18}\times 5x)$$

Multiply \frac{1}{18} and 5 to get \frac{5}{18}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{3}+\frac{5}{18}x)$$

Combine \frac{x}{3} and \frac{5}{18}x to get \frac{11}{18}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11}{18}x)$$

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

$$\frac{11}{18}x^{1-1}$$

Subtract 1 from 1.

$$\frac{11}{18}x^{0}$$

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

$$\frac{11}{18}\times 1$$

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

$$\frac{11}{18}$$