Solve 1/2(x)^(2)-2/3x\div2/3x | Equatix

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Question

$$1/2 { x }^{ 2 } -2/3x \div 2/3x$$

Evaluate

$\frac{7x^{2}}{18}$

Solution Steps

Express $\frac{\frac{\frac{2}{3}x}{2}}{3}$ as a single fraction.

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

Multiply $2$ and $3$ to get $6$.

$$\frac{1}{2}x^{2}-\frac{\frac{2}{3}x}{6}x$$

Divide $\frac{2}{3}x$ by $6$ to get $\frac{1}{9}x$.

$$\frac{1}{2}x^{2}-\frac{1}{9}xx$$

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{1}{2}x^{2}-\frac{1}{9}x^{2}$$

Combine $\frac{1}{2}x^{2}$ and $-\frac{1}{9}x^{2}$ to get $\frac{7}{18}x^{2}$.

$$\frac{7}{18}x^{2}$$

Show Solution

Differentiate w.r.t. x

$\frac{7x}{9}$

Steps Using Definition of a Derivative

Express $\frac{\frac{\frac{2}{3}x}{2}}{3}$ as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}-\frac{\frac{2}{3}x}{2\times 3}x)$$

Multiply $2$ and $3$ to get $6$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}-\frac{\frac{2}{3}x}{6}x)$$

Divide $\frac{2}{3}x$ by $6$ to get $\frac{1}{9}x$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}-\frac{1}{9}xx)$$

Multiply $x$ and $x$ to get $x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}-\frac{1}{9}x^{2})$$

Combine $\frac{1}{2}x^{2}$ and $-\frac{1}{9}x^{2}$ to get $\frac{7}{18}x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{18}x^{2})$$

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

$$2\times \frac{7}{18}x^{2-1}$$

Multiply $2$ times $\frac{7}{18}$.

$$\frac{7}{9}x^{2-1}$$

Subtract $1$ from $2$.

$$\frac{7}{9}x^{1}$$

For any term $t$, $t^{1}=t$.

$$\frac{7}{9}x$$