Solve x/20+x/80+x/40

$$\frac { x } { 20 } + \frac { x } { 80 } + \frac { x } { 40 }$$

Evaluate

$$\frac{7x}{80}$$

Solution Steps

Combine \frac{x}{20} and \frac{x}{80} to get \frac{1}{16}x.

$$\frac{1}{16}x+\frac{x}{40}$$

Combine \frac{1}{16}x and \frac{x}{40} to get \frac{7}{80}x.

$$\frac{7}{80}x$$

Differentiate w.r.t. x

$$\frac{7}{80} = 0.0875$$

Steps Using Definition of a Derivative

Combine \frac{x}{20} and \frac{x}{80} to get \frac{1}{16}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{16}x+\frac{x}{40})$$

Combine \frac{1}{16}x and \frac{x}{40} to get \frac{7}{80}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{80}x)$$

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

$$\frac{7}{80}x^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{80}x^{0}$$

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

$$\frac{7}{80}\times 1$$

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

$$\frac{7}{80}$$