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Implicit differentiation is a different way to find the derivative when $y$ is "stuck" inside an equation and you can't or don't want to isolate it as $y = \dots$. Always treat $y$...
$h x = \frac{1}{f x }$ $$ \begin{array}{0} \text{cosec} \space x = \frac{1}{\sin x} \\ \text{cosec}^2 \space x = \frac{1}{\sin^2 x} \\ \sec x = \frac{1}{\cos x} \\ \cot x = \frac{1...
$$ \begin{array}{0} \frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt} \\ \frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx} \\ \frac{dy}{dx} = \frac{dy}{dx} \end{array} $$
$$ \begin{array}{0} y = \frac{u x }{v x } \\ \frac{dy}{dx} = \frac{v x u' x u x v' x }{v x ^2} \end{array} $$
$$ \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx} $$ Chain rule is used to decompose working with complex equations within differentiation much easier. It allows you to substit...
Exponential Rules $$ \begin{array}{0} \frac{d}{dx} e^x = e^x \\ \frac{d}{dx} e^{kx} = ke^{kx} \\ \frac{d}{dx} a^x = a^x \ln a \\ \frac{d}{dx} a^{kx} = a^{kx} k \ln a \end{array} $$...
$$ \begin{array}{0} y = uv \\ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} \end{array} $$ Examples $y = x \sin x$ $$ \begin{array}{0} y = x \sin x \\ u = x \\ v = \sin x \\ \f...
$$ \frac{dx}{dy} = \frac{1}{\frac{dy}{dx}} $$ Just like you can get $x$ from $y$ by getting the reciprocal of $y$, you can do the same for $\frac{dx}{dy}$ , allowing you to easily...