Question

Determine a derivada dy/dx das funções definidas implicitamente pelas equações:
a) z = xy sen xz

Answer 1

$y=f(x,z)=\dfrac{z}{x\sin xz}\\ \\ \dfrac{\partial y}{\partial x}=-\dfrac{z\dfrac{\partial }{\partial x}(x\sin xz) }{(x\sin xz)^2}\\ \\ \\ \boxed{\dfrac{\partial y}{\partial x}=-\dfrac{z(\sin xz -xz\cos xz)}{(x\sin xz)^2}}$