Given that $tany= x^2$ , what is the value of $dy/dx$ ?

Question

3003 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-07T03:28:26

$dy/dx = (2x)/sec^2y$

We write $tany$ as $siny/cosy$ and differentiate using the quotient rule (with respect to $x$ ) .

$siny/cosy = x^2$

$(cosy(cosy)(dy/dx) - (-siny xx siny)dy/dx)/(cosy)^2 = 2x$

$(cos^2y(dy/dx) + sin^2y(dy/dx))/cos^2y = 2x$

We use the identity $sin^2beta + cos^2beta = 1$ to simplify further...

$(dy/dx)/(cos^2y) = 2x$

Use the identity $sectheta = 1/costheta$ ...

$dy/dxsec^2y = 2x$

$dy/dx = (2x)/sec^2y$

Hopefully this helps!

Given that tany= x^2tany= x^2, what is the value of dy/dxdy/dx?