Calculus Examples

$0.007184 x^{0.425} y^{0.725}$

Step 1

Since $0.007184 x^{0.425}$ is constant with respect to $y$ , the derivative of $0.007184 x^{0.425} y^{0.725}$ with respect to $y$ is $0.007184 x^{0.425} \frac{d}{d y} [y^{0.725}]$ .

$0.007184 x^{0.425} \frac{d}{d y} [y^{0.725}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = 0.725$ .

$0.007184 x^{0.425} (0.725 y^{- 0.275})$

Step 3

Multiply $0.725$ by $0.007184$ .

$0.0052084 x^{0.425} y^{- 0.275}$

Step 4

Simplify.

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Step 4.1

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

$0.0052084 x^{0.425} \frac{1}{y^{0.275}}$

Step 4.2

Combine terms.

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Step 4.2.1

Combine $0.0052084$ and $\frac{1}{y^{0.275}}$ .

$x^{0.425} \frac{0.0052084}{y^{0.275}}$

Step 4.2.2

Combine $x^{0.425}$ and $\frac{0.0052084}{y^{0.275}}$ .

$\frac{x^{0.425} \cdot 0.0052084}{y^{0.275}}$

Step 4.2.3

Move $0.0052084$ to the left of $x^{0.425}$ .

$\frac{0.0052084 x^{0.425}}{y^{0.275}}$