Calculus Examples

$- \frac{5 x^{2}}{4 y^{2}}$

Step 1

This derivative could not be completed using the quotient rule. Mathway will use another method.

Step 2

Since $- \frac{5}{4 y^{2}}$ is constant with respect to $x$ , the derivative of $- \frac{5 x^{2}}{4 y^{2}}$ with respect to $x$ is $- \frac{5}{4 y^{2}} \frac{d}{d x} [x^{2}]$ .

$- \frac{5}{4 y^{2}} \frac{d}{d x} [x^{2}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$- \frac{5}{4 y^{2}} (2 x)$

Step 4

Simplify terms.

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Step 4.1

Multiply $2$ by $- 1$ .

$- 2 \frac{5}{4 y^{2}} x$

Step 4.2

Combine $- 2$ and $\frac{5}{4 y^{2}}$ .

$\frac{- 2 \cdot 5}{4 y^{2}} x$

Step 4.3

Multiply $- 2$ by $5$ .

$\frac{- 10}{4 y^{2}} x$

Step 4.4

Combine $\frac{- 10}{4 y^{2}}$ and $x$ .

$\frac{- 10 x}{4 y^{2}}$

Step 4.5

Cancel the common factor of $- 10$ and $4$ .

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Step 4.5.1

Factor $2$ out of $- 10 x$ .

$\frac{2 (- 5 x)}{4 y^{2}}$

Step 4.5.2

Cancel the common factors.

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Step 4.5.2.1

Factor $2$ out of $4 y^{2}$ .

$\frac{2 (- 5 x)}{2 (2 y^{2})}$

Step 4.5.2.2

Cancel the common factor.

$\frac{2 (- 5 x)}{2 (2 y^{2})}$

Step 4.5.2.3

Rewrite the expression.

$\frac{- 5 x}{2 y^{2}}$

Step 4.6

Move the negative in front of the fraction.

$- \frac{5 x}{2 y^{2}}$