Solve 3x/14+5x/14

$$\frac { 3 x } { 14 } + \frac { 5 x } { 14 }$$

Evaluate

$$\frac{4x}{7}$$

Short Solution Steps

Since \frac{3x}{14} and \frac{5x}{14} have the same denominator, add them by adding their numerators.

$$\frac{3x+5x}{14}$$

Combine like terms in 3x+5x.

$$\frac{8x}{14}$$

Divide 8x by 14 to get \frac{4}{7}x.

$$\frac{4}{7}x$$

Differentiate w.r.t. x

$$\frac{4}{7} = 0.5714285714285714$$

Steps Using Definition of a Derivative

Since \frac{3x}{14} and \frac{5x}{14} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+5x}{14})$$

Combine like terms in 3x+5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x}{14})$$

Divide 8x by 14 to get \frac{4}{7}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{7}x)$$

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

$$\frac{4}{7}x^{1-1}$$

Subtract 1 from 1.

$$\frac{4}{7}x^{0}$$

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

$$\frac{4}{7}\times 1$$

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

$$\frac{4}{7}$$