Algebra Examples

$y = \frac{3 x \cdot 10^{8}}{x}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (\frac{3 x \cdot 10^{8}}{x})$

Step 2

The derivative of $y$ with respect to $x$ is $y'$ .

$y'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

Reduce the expression by cancelling the common factors.

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Step 3.1.1

Raise $10$ to the power of $8$ .

$\frac{d}{d x} [\frac{3 x \cdot 100000000}{x}]$

Step 3.1.2

Multiply $100000000$ by $3$ .

$\frac{d}{d x} [\frac{300000000 x}{x}]$

Step 3.1.3

Cancel the common factor of $x$ .

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Step 3.1.3.1

Cancel the common factor.

$\frac{d}{d x} [\frac{300000000 x}{x}]$

Step 3.1.3.2

Divide $300000000$ by $1$ .

$\frac{d}{d x} [300000000]$

Step 3.2

Since $300000000$ is constant with respect to $x$ , the derivative of $300000000$ with respect to $x$ is $0$ .

$0$

Step 4

Reform the equation by setting the left side equal to the right side.

$y' = 0$

Step 5

Replace $y'$ with $\frac{d y}{d x}$ .

$\frac{d y}{d x} = 0$