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3 years ago

Can someone make a thesis statement out of this?

Advanced Placement (AP)

1 answer:

Lady bird [3.3K]3 years ago

7 0

When you create a thesis, you always want there to be proof that you can use.

Also, you should make your 3-4 body paragraphs before you create your thesis so then you can create a wonderful claim that does follow your evidence.

One thesis I created with the information given is: The Civil War and Reconstruction period in the United States is the "Second American Revolution" due to historians.

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3 years ago

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3 years ago

Find dy/dx if 3xy=4x+y^2

ElenaW [278]

Hi there!

We can use implicit differentiation with respect to x:

$3xy = 4x + y^2$

If a term with 'y' is differentiated, a 'dy/dx' must be included.

We can differentiate each term separately for the explanation.

3xy

We must use the power rule since 'x' and 'y' are both in this term.

Power rule:

$f(x) * g(x) = f'(x)g(x) + g'(x)f(x)$

$3xy \\\\f(x) = 3x\\g(x) = y \\\\f'(x)g(x) + g'(x)f(x) = 3y + 3x\frac{dy}{dx}$

Now, we can do the others.

4x

This is a normal power rule derivative.

$f(x) = 4x\\f'(x) = 4$

y²

Since we are not differentiating with respect to y, we must include 'dy/dx'.

$f(x) = y^2\\f'(x) = 2y\frac{dy}{dx}$

Combine the above:

$3y + 3x\frac{dy}{dx} = 4 + 2y\frac{dy}{dx}$

Rearrange to solve for dy/dx.

Move dy/dx to one side:

$3x\frac{dy}{dx} - 2y\frac{dy}{dx} = 4 + 3y \\\\$

Factor out dy/dx and divide:

$\frac{dy}{dx}(3x- 2y) = 4 + 3y \\\\\boxed{\frac{dy}{dx} = \frac{4+3y}{3x-2y}}$

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2 years ago