Solve 2x*5/3+x

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

Evaluate

$$\frac{13x}{3}$$

Solution Steps

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

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

Multiply 2 and 5 to get 10.

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

Combine \frac{10}{3}x and x to get \frac{13}{3}x.

$$\frac{13}{3}x$$

Differentiate w.r.t. x

$$\frac{13}{3} = 4\frac{1}{3} = 4.333333333333333$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 5 to get 10.

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

Combine \frac{10}{3}x and x to get \frac{13}{3}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{13}{3}x)$$

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

$$\frac{13}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{13}{3}x^{0}$$

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

$$\frac{13}{3}\times 1$$

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

$$\frac{13}{3}$$