Calculus Examples

$y = a^{f (x)}$

Differentiate both sides of the equation.

$\frac{d}{d y} (y) = \frac{d}{d y} (a^{f (x)})$

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

$1$

Since $a^{f (x)}$ is constant with respect to $y$ , the derivative of $a^{f (x)}$ with respect to $y$ is $0$ .

$0$

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

$1 = 0$

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

No solution

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

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