How to solve 1/2V(-2/5V)(0.8V)

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 1/2V(-2/5V)(0.8V) | Equatix

Question

$$1/2V(-2/5V)(0.8V)$$

Evaluate

$-\frac{4V^{3}}{25}$

Solution Steps

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

$$\frac{1}{2}V^{2}\times \frac{-2}{5}\times 0.8V$$

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$\frac{1}{2}V^{3}\times \frac{-2}{5}\times 0.8$$

Fraction $\frac{-2}{5}$ can be rewritten as $-\frac{2}{5}$ by extracting the negative sign.

$$\frac{1}{2}V^{3}\left(-\frac{2}{5}\right)\times 0.8$$

Multiply $\frac{1}{2}$ times $-\frac{2}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-2\right)}{2\times 5}V^{3}\times 0.8$$

Do the multiplications in the fraction $\frac{1\left(-2\right)}{2\times 5}$.

$$\frac{-2}{10}V^{3}\times 0.8$$

Reduce the fraction $\frac{-2}{10}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{1}{5}V^{3}\times 0.8$$

Convert decimal number $0.8$ to fraction $\frac{8}{10}$. Reduce the fraction $\frac{8}{10}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{1}{5}V^{3}\times \frac{4}{5}$$

Multiply $-\frac{1}{5}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4}{5\times 5}V^{3}$$

Do the multiplications in the fraction $\frac{-4}{5\times 5}$.

$$\frac{-4}{25}V^{3}$$

Fraction $\frac{-4}{25}$ can be rewritten as $-\frac{4}{25}$ by extracting the negative sign.

$$-\frac{4}{25}V^{3}$$

Show Solution

Differentiate w.r.t. V

$-\frac{12V^{2}}{25}$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{1}{2}V^{2}\times \frac{-2}{5}\times 0.8V)$$

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{1}{2}V^{3}\times \frac{-2}{5}\times 0.8)$$

Fraction $\frac{-2}{5}$ can be rewritten as $-\frac{2}{5}$ by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{1}{2}V^{3}\left(-\frac{2}{5}\right)\times 0.8)$$

Multiply $\frac{1}{2}$ times $-\frac{2}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{1\left(-2\right)}{2\times 5}V^{3}\times 0.8)$$

Do the multiplications in the fraction $\frac{1\left(-2\right)}{2\times 5}$.

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{-2}{10}V^{3}\times 0.8)$$

Reduce the fraction $\frac{-2}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\mathrm{d}}{\mathrm{d}V}(-\frac{1}{5}V^{3}\times 0.8)$$

Convert decimal number $0.8$ to fraction $\frac{8}{10}$. Reduce the fraction $\frac{8}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\mathrm{d}}{\mathrm{d}V}(-\frac{1}{5}V^{3}\times \frac{4}{5})$$

Multiply $-\frac{1}{5}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{-4}{5\times 5}V^{3})$$

Do the multiplications in the fraction $\frac{-4}{5\times 5}$.

$$\frac{\mathrm{d}}{\mathrm{d}V}(\frac{-4}{25}V^{3})$$

Fraction $\frac{-4}{25}$ can be rewritten as $-\frac{4}{25}$ by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}V}(-\frac{4}{25}V^{3})$$

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

$$3\left(-\frac{4}{25}\right)V^{3-1}$$

Multiply $3$ times $-\frac{4}{25}$.

$$-\frac{12}{25}V^{3-1}$$

Subtract $1$ from $3$.

$$-\frac{12}{25}V^{2}$$

Show Solution

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Example

Question

Evaluate

Solution Steps

Differentiate w.r.t. V

Steps Using Definition of a Derivative