Question

If y=e3x-e2x/e3x+e2x then dy/dx is

Answer 1

Answer:

2e^2x.e^3x / (e^3x + e^2x)²

Step-by-step explanation:

Here, y= e^3x - e^2x / e^3x + e^2x

Now,

( dy/dx )

=>

(e^3x+e^2x)(3e^3x-2e^2x) - (e^3x-e^2x)(3e^3x+2e^2x)

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(e^3x + e^2x)²

=>

3e^6x-2e^3x.e^2x+3e^2x.e^3x-2e^4x

- ( 3e^6x+2e^3x.e^2x-3e^2x.e^3x-2e^4x )

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(e^3x + e^2x)²

=>

3e^6x-2e^3x.e^2x+3e^2x.e^3x-2e^4x

-3e^6x-2e^3x.e^2x+3e^2x.e^3x+2e^4x

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(e^3x + e^2x)²

=>

-4e^3x.e^2x+6e^2x.e^3x

____________________

(e^3x + e^2x)²

=>

2e^2x.e^3x

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(e^3x + e^2x)²