Solve frac{sqrt{x}*sqrt[3]{x^2}}{{x}^frac{1{6}}}

$$\frac{ \sqrt{ x } \times \sqrt[3]{ { x }^{ 2 } } }{ { x }^{ \frac{ 1 }{ 6 } } }$$

Evaluate

$$x$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\sqrt{x}\sqrt[3]{x^{2}}}{\sqrt[6]{x}}$$

Cancel out \sqrt[6]{x} in both numerator and denominator.

$$\sqrt[3]{x}\sqrt[3]{x^{2}}$$

Expand the expression.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Factor the expressions that are not already factored in \frac{\sqrt{x}\sqrt[3]{x^{2}}}{x^{\frac{1}{6}}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\sqrt{x}\sqrt[3]{x^{2}}}{\sqrt[6]{x}})$$

Cancel out \sqrt[6]{x} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt[3]{x}\sqrt[3]{x^{2}})$$

Expand the expression.

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

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.

$$1$$