# Questions tagged [implicit-differentiation]

For questions on finding and evaluating derivatives when a function is defined implicitly.

949 questions
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### Why does implicit derivative change after division? (For $\sec(x)+\tan(y) = \sec(x)*\tan(y))$)

If I take the implicit derivative without dividing, I get the solution $\frac{dy}{dx} = (\sec(x) \tan(x) \cos(y)) \frac{\cos(y)-\sin(y))}{\sec(x)-1}$. If I divide both sides by $\sec(x) \tan(y)$, I ...
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### A particle moves along the curve… Find component of acceleration [on hold]

differentiation of vector to find components of velocity and accelration (https://i.stack.imgur.com/djAtB.jpg)
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### Implicit differentiation applied to $z=\frac{1}{y}(f(ax+y)+g(ax-y)).$

I'm trying show that $$\frac{\partial^2z}{\partial x^2}=\frac{a^2}{y^2}\frac{\partial}{\partial y}( y^2\frac{\partial z}{\partial y})$$knowing that: $$z=\frac{1}{y}(f(ax+y)+g(ax-y)).$$ I know that,...
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### Can implicit differentiation be used when differentiating with respect to the dependent variable?

EDIT: I forgot to add that I desperately need clarification on this as I will be sitting an exam shortly. Sorry in advance if this does not comply with guidelines -- I'm still new to this site. I'll ...
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### Implicit Function Theorem with $x^2+y^2+z^2=\psi(ax+by+cz)$

Given the equation $x^2+y^2+z^2=\psi(ax+by+cz)$, with $a,b,c\in\mathbb{R},\ c\neq 0$, and $\psi:\mathbb{R}\to\mathbb{R}$ that satisfies $\psi\in C^2,\ \psi(0)=0,\ \psi'(0)\neq0$, prove that in a ...
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### Implicit multivariable derivative in polar coordinates

Determine the first and second orders derivatives of $y = f(x)$ determined implicity by $$\ln\sqrt{x^2 + y^2} = \alpha~\arctan\frac{y}{x}$$ Now, notice that in polar coordinates, the ...
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### Calculus - Implicit Curve - rearranging derivative equation

I'm new to this community, so please bear with me if I make a mistake following rules and conventions, and thanks in advance. I'm currently learning - following along from this video ("Implicit ...
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### Differentiating with respect to size of index

I have the following function: $$a\sum_{i=1}^{n}x_i.$$ I wish to differentiate with respect to $n$. If all $x_i$s were the same, this problem would be trivial, obviously. Can anyone help?
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