Find dy/dx xy=6 - MathMaster

$x y = 6$

Differentiate both sides of the equation.

$\frac{d}{d x} (x y) = \frac{d}{d x} (6)$

Differentiate the left side of the equation.

Tap for more steps…

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = x$ and $g (x) = y$ .

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

Rewrite $\frac{d}{d x} [y]$ as $\frac{d}{d x} [y]$ .

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

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

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

Multiply $y$ by $1$ .

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

Since $6$ is constant with respect to $x$ , the derivative of $6$ with respect to $x$ is $0$ .

$0$

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

$x y' + y = 0$

Solve for $y'$ .

Tap for more steps…

Subtract $y$ from both sides of the equation.

$x y' = - y$

Divide each term by $x$ and simplify.

Tap for more steps…

Divide each term in $x y' = - y$ by $x$ .

$\frac{x y'}{x} = \frac{- y}{x}$

Cancel the common factor of $x$ .

Tap for more steps…

Cancel the common factor.

$\frac{x y'}{x} = \frac{- y}{x}$

Divide $y'$ by $1$ .

$y' = \frac{- y}{x}$

Move the negative in front of the fraction.

$y' = - \frac{y}{x}$

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

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

Find dy/dx xy=6

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store