Calculus Examples

$y = x \tan (x)$

Step 1

Differentiate both sides of the equation.

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

Step 2

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

$1$

Step 3

Since $x \tan (x)$ is constant with respect to $y$ , the derivative of $x \tan (x)$ with respect to $y$ is $0$ .

$0$

Step 4

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

$1 = 0$

Step 5

Since $1 \neq 0$ , there are no solutions.

No solution

Step 6

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

$\frac{d ?}{d y}$