My Twelfth Problem

Calculus Level 3

$\large \tan (\ln(x+y))=\sinh^{10}(x+y)$

Given the above, evaluate $\dfrac{dy}{dx}$ for $x=\dfrac{\pi}{6}$ and $-1<y<0$ .

The answer is -1.

1 solution

Daniel Ellesar
Nov 2, 2015

Any x to y graph that takes the form $f(x+y)=0$ is linear with a constant gradient of $-1$ (unless it has weird things like mods that could change the $x+y$ bit), where the axis intercepts are the solution(s) for $z$ to the equation $f(z)=0$ . A graph of this particular equation takes the form of infinite parallel lines, each with a gradient of $-1$ , where the axis intercepts are the solutions for $z$ to the equation $tan[ln(z)]-sinh^{10}(z)=0$ (which I can't do in my head).

My Twelfth Problem

The answer is -1.

1 solution

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