If y = f(x) is an odd differentiable function defined on $(-\infty, \infty)$ such that f'(3) = -2, then f'(-3) equals

-2

Since f(x) is an odd differentiable function defined on R. Therefore,

$f(-x)=-f(x)$ for all  $x \in R$

Differentiating both sides w.r.t. x, we get

$-f'(-x)=-f'(x)$  for all  $x \in R$

$\Rightarrow f'(-x)=f'(x)$  for all  $x \in R$

$\Rightarrow f'(-3)=f'(3)=-2$

ALITER We know that the derivative of a differentiable odd function is an even function. Therefore, f'(x) is an even function. Hence,

$f'(-3)=f'(3)=-2$