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The curve C has the equation ye ^(–2x) = 2x + y^2 . Find dy/dx in terms of x and y.

differentiate both side with respect to x : (dy/dx)e^(-2x)+y(-2e^(-2x)) = 2+2y(dy/dx) rearrange it : (-2y+e^(-2x))(dy/dy) = 2 + 2ye^(-2x) ==> dy/dx = ( 2 + 2ye^(-2x) ) / ( -2y+e^(-2x) )
JC
Answered by Jimmy C. • Maths tutor
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How to write an EPQ introduction

The first thing to do is to establish the purpose of the essay – in doing this, we want to break down the question that is being answered and examine the components of it. This sounds like it is just an exer...
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How does Shakespeare discuss the themes of disguise in Twelfth Night?

Disguise is the key theme in Twelfth Night and this question therefore opens up a discussion with a lot of scope. Details about characters can be mentioned and it can also be linked to other themes. Starting...
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Integration of ln(x)

Let f denote an integral sign, I will write the integrand in square brackets. We can use integration by parts to integrate ln(x), the "trick" here is to imagin ln(x) as 1 x ln(x). Integration by pa...
AS
Answered by Amelia S. • Maths tutor
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Use integration by parts to find the value of the indefinite integral (1/x^3)lnx ; integration with respect to dx

Let f denote an integral sign, I will write the integrand in square brackets. The formula for integration by parts is given by: f [(u)(dv/dx)]dx = uv - f [((du/dx)(v)]dxTo apply this rule we imagine our inte...
AS
Answered by Amelia S. • Maths tutor
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