Question

Suppose that y is a differentiable function of x which satisfies the equation
5y2+7xsiny=cos5x
Use the method of implicit differentiation to find dxdy.

Answer 1

if someone knows how to do this, could you briefly show me the steps that go along with it

Answer 2

Solution: differentiate implicitly so it will become: 10y dx/dy + 7x cosy dx/dy + 7 siny = -5 sin 5x (you use product rule in differentiating 7xsiny).

then, you group like terms, so the answer will be: 10y dx/dy + 7x cosy dx/dy = -5sin5x - 7 siny

then factor out dx/dy : dx/dy(10y + 7x cosy) = - 5 sin5x - 7siny

then divide 10y+7x cosy both sides to cancel the 10y+7xcosy coming up with your answer

(-5sin5x - 7siny) / ( 10y + 7x cosy)

Answer 3

apparently there is a mistake in this?

Answer 4

what mistake ? ^^

Answer 5

im not sure, im trying to figure it out right now but the answer is apparently incorrect

Answer 6

rechecked my answer if you mean 5y^2 in your question not 5y*2 then my answer is corect ^^