dx/dy and dy/dx confusion!!

Hey I wonder if you can help - I'm having trouble with this question...




$\ x = \sqrt {y^2+3y}$

I realise that the rule that dy/dx is the reciprocal of dx/dy, but I am only managing to get dx/dy in terms of y's - therefore I can't just flip my final fraction to get dy/dx since it'll all be in terms of y!! My final answer for dx/dy (in terms of y) was:

$\frac{dx}{dy} = \frac{(2y+3)}{2 \sqrt {y(y+3)}}$

But how to get into dy/dx!!!???

Thanks

Hey I wonder if you can help - I'm having trouble with this question...




$\ x = \sqrt {y^2+3y}$

I realise that the rule that dy/dx is the reciprocal of dx/dy, but I am only managing to get dx/dy in terms of y's - therefore I can't just flip my final fraction to get dy/dx since it'll all be in terms of y!! My final answer for dx/dy (in terms of y) was:

$\frac{dx}{dy} = \frac{(2y+3)}{2 \sqrt {y(y+3)}}$

But how to get into dy/dx!!!???

Thanks

just use the value of y=1 you don't need dy/dx in terms of x

Of course! I'm so dumb lol.... so do I just plug in 1 to the final dx/dy I got below? And then that will tell me the gradient at that point?

just filp the fraction that you got for dx/dy to get dy/dx in terms of y. then put in y=1

Great! Thanks very much all!