Solve 4/5xsqrt{4}

$$\frac{ 4 }{ 5 } x \sqrt{ 4 }$$

Evaluate

$$\frac{8x}{5}$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{4}{5}x\times 2$$

Express \frac{4}{5}\times 2 as a single fraction.

$$\frac{4\times 2}{5}x$$

Multiply 4 and 2 to get 8.

$$\frac{8}{5}x$$

Differentiate w.r.t. x

$$\frac{8}{5} = 1\frac{3}{5} = 1.6$$

Steps Using Definition of a Derivative

Calculate the square root of 4 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{5}x\times 2)$$

Express \frac{4}{5}\times 2 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 2}{5}x)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{5}x)$$

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

$$\frac{8}{5}x^{1-1}$$

Subtract 1 from 1.

$$\frac{8}{5}x^{0}$$

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

$$\frac{8}{5}\times 1$$

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

$$\frac{8}{5}$$