Solve 1/(frac{1{sqrt{x}})^2}

$$\frac { 1 } { ( \frac { 1 } { \sqrt { x } } ) ^ { 2 } }$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To raise \frac{1}{\sqrt{x}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1^{2}}{\left(\sqrt{x}\right)^{2}}})$$

Divide 1 by \frac{1^{2}}{\left(\sqrt{x}\right)^{2}} by multiplying 1 by the reciprocal of \frac{1^{2}}{\left(\sqrt{x}\right)^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(\sqrt{x}\right)^{2}}{1^{2}})$$

Calculate \sqrt{x} to the power of 2 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{1^{2}})$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{1})$$

Anything divided by one gives itself.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$

Evaluate

$$x$$