3 years ago

What is the value of x? Help me please

Mathematics

1 answer:

Basile [38]3 years ago

5 0

168 degrees
180-12=168

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What is your question please

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3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Cbegin%7Bequation%7D%5Ctext%20%7B%20Question%3A%20If%20%7D%20%5Cln%20%28x%2By%29%3D4%20%5Cti

Art [367]

I think you meant to say

$\ln(x+y) = 4xy$

and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.

Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives

$\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}$

$\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}$

Note that when x = 0 and y = 1, we have dy/dx = 3.

Differentiate both sides again with respect to x :

$\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}$