# Tagged Questions

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### How do I evaluate this implicit differentiation?

I was reading a Classical Mechanics book. The author was deriving Kepler's equation. He was changing variables for integrating the stuff later. Here's my reproduction of that figure. $N$ is the ...
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### Implicitly differentiate $e^y \cos(x) = 1 + \sin(xy)$

I can differentiate one side of the equation, but I dont know how to deal with sin(xy)
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### Finding the Derivative of a Derivative

Let $x^3+y^3=9$. Find $y''(x)$ at the point $(2,1)$. I keep getting $3x^2+(3y^2)y'=0$ as the first derivative then simplify that down to $-3x^2/(3y^2).$ But after that I keep getting ...
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### Use implicit differentiation to find an equation of the tangent line to the curve

$$x^2+xy+y^2=3, (1,1)$$ I got the derivative as.. $$\frac{2x-2}{x+4}$$ But when I plug in the points I get the equation $y=x/2+2$ which is wrong. Is my derivative wrong? Or am I making a mistake ...
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### Implicit form of general equation

Find, in implicit form, the general solution of the differential equation: $$\frac{dy}{dx}= \frac{2y^4e^{2x}}{3\left(e^{2x}+7\right)^2}$$ I am struggling to make any sense of this. What I have ...
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### dy/dx of $\;e^{xy^2}= 2x + y\;$- should I just calculate derivative of both sides? [closed]

should I just derive both sides of the equation? thanks
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### Find the slope of the tangent line $\ln(3y-5)+x=y^2$ at $(4,2)$ [closed]

Find the slope of the tangent line $\ln(3y-5)+x=y^2$ at $(4,2)$. I need help with differentiating the ln part but a complete step by step answer would help.
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### Differential Calculus, Slope at a Given Point [closed]

If $$3x^2 + 2xy + y^2 = 2$$ then what is the value of $dy/dx$ when $x = 1$?
The line that is normal to the curve $x^2+3xy-4y^2=0$ at $(6,6)$ intersects the curve at what other point? If I implicitly differentiate this curve, I will get the equation of the slope: ...