How to solve (x)/(2root(3,x))

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x)/(2root(3,x)) | Equatix

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Question

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

Differentiate w.r.t. x

$\frac{1}{3\sqrt[3]{x}}$

Steps Using Definition of a Derivative

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

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

Cancel out $\sqrt[3]{x}$ in both numerator and denominator.

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

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

$$\frac{2}{3}\times \frac{1}{2}x^{\frac{2}{3}-1}$$

Multiply $\frac{2}{3}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{1}{3}x^{\frac{2}{3}-1}$$

Subtract $1$ from $\frac{2}{3}$.

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

Show Solution

Evaluate

$\frac{x^{\frac{2}{3}}}{2}$