Find the Derivative - d/dx (dy)/(dx)

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

Step 1

Cancel the common factor of $d$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Since $y$ is constant with respect to $x$ , the derivative of $\frac{y}{x}$ with respect to $x$ is $y \frac{d}{d x} [\frac{1}{x}]$ .

$y \frac{d}{d x} [\frac{1}{x}]$

Step 3

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$y \frac{d}{d x} [x^{- 1}]$

Step 4

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

$y (- x^{- 2})$

Step 5

Simplify.

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

$y (- \frac{1}{x^{2}})$

Combine $y$ and $\frac{1}{x^{2}}$ .

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