Consider the function f(x,y)=x^2+y^2 where x=sin2θ and y=cos2θ
df/dθ is given by?
I know this involves the chain rule and trig id.
But I'm still not getting it
Kindly assist.
Since $\displaystyle f$ is a function of $\displaystyle x \; \text{and}\; y$ and $\displaystyle x \; \text{and}\; y$ are functions of $\displaystyle \theta$, then $\displaystyle f$ is a function of $\displaystyle \theta$ so $\displaystyle \frac{df}{d \theta}$ makes sense. The chain rule is
$\displaystyle (1)\;\;\;\;\;\frac{df}{d \theta} = \frac{\partial f}{\partial x} \frac{d x}{d \theta} + \frac{\partial f}{\partial y} \frac{dy} {d \theta} $.
So calculate all of the derivatives
$\displaystyle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{d x}{ d \theta} \; \text{and}\;\frac{d y}{d \theta} $
and substitute them into (1). Finally, use your expressions for $\displaystyle x\; \text{and}\; y$ to get your final answer.