Calculus Examples

$0.25 X^{0.25} y^{0.75}$

Step 1

Since $0.25 y^{0.75}$ is constant with respect to $X$ , the derivative of $0.25 X^{0.25} y^{0.75}$ with respect to $X$ is $0.25 y^{0.75} \frac{d}{d X} [X^{0.25}]$ .

$0.25 y^{0.75} \frac{d}{d X} [X^{0.25}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d X} [X^{n}]$ is $n X^{n - 1}$ where $n = 0.25$ .

$0.25 y^{0.75} (0.25 X^{- 0.75})$

Step 3

Multiply $0.25$ by $0.25$ .

$0.0625 y^{0.75} X^{- 0.75}$

Step 4

Simplify.

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Step 4.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$0.0625 y^{0.75} \frac{1}{X^{0.75}}$

Step 4.2

Combine terms.

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Step 4.2.1

Combine $0.0625$ and $\frac{1}{X^{0.75}}$ .

$y^{0.75} \frac{0.0625}{X^{0.75}}$

Step 4.2.2

Combine $y^{0.75}$ and $\frac{0.0625}{X^{0.75}}$ .

$\frac{y^{0.75} \cdot 0.0625}{X^{0.75}}$

Step 4.2.3

Move $0.0625$ to the left of $y^{0.75}$ .

$\frac{0.0625 y^{0.75}}{X^{0.75}}$