Solve x/sqrt{5+2-3}

$$\frac{ x }{ \sqrt{ 5+2-3 } }$$

Evaluate

$$\frac{x}{2}$$

Solution Steps

Add 5 and 2 to get 7.

$$\frac{x}{\sqrt{7-3}}$$

Subtract 3 from 7 to get 4.

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

Calculate the square root of 4 and get 2.

$$\frac{x}{2}$$

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\sqrt{7-3}})$$

Subtract 3 from 7 to get 4.

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

Calculate the square root of 4 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{2})$$

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

$$\frac{1}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

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

$$\frac{1}{2}\times 1$$

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

$$\frac{1}{2}$$