Question #7840

Implicit Differentiation of the following

1.) (3xy+7)^2=18y

2.) 4y^2=(3x-2)/(3x+2)

3.)x=sin y

4.) x+cot(xy)=1

5.) x^4+sin y=x^3y^5

1.) (3xy+7)^2=18y

2.) 4y^2=(3x-2)/(3x+2)

3.)x=sin y

4.) x+cot(xy)=1

5.) x^4+sin y=x^3y^5

Expert's answer

1.

We've created video explaining how to solve this problem. Please take a look!

2. 4y^2=(3x-2)/(3x+2)here we can easily derive expression for y:

y=+-0.5sqty((3x-2)/(3x+2)) and then derive it as usual

3. x=sin y

here we can also derive expression for y:

y=sin^{-1}(x)

so y'=1/sqrt(1-x^2)

We've created video explaining how to solve this problem. Please take a look!

2. 4y^2=(3x-2)/(3x+2)here we can easily derive expression for y:

y=+-0.5sqty((3x-2)/(3x+2)) and then derive it as usual

3. x=sin y

here we can also derive expression for y:

y=sin

so y'=1/sqrt(1-x^2)

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