If f(x) is an odd differentiable function def | vedclass

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(C) Given that $f(x)$ is an odd differentiable function. By definition of an odd function, $f(-x) = -f(x)$. Differentiating both sides with respect to

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$2$

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(C) Given that $f(x)$ is an odd differentiable function. By definition of an odd function, $f(-x) = -f(x)$. Differentiating both sides with respect to $x$ using the chain rule: $\frac{d}{dx}[f(-x)] = \frac{d}{dx}[-f(x)]$ $-f^{\prime}(-x) = -f^{\prime}(x)$ $f^{\prime}(-x) = f^{\prime}(x)$ This shows that the derivative of an odd function is an even function. Now, substitute $x = 3$ into the equation $f^{\prime}(-x) = f^{\prime}(x)$: $f^{\prime}(-3) = f^{\prime}(3)$ Since it is given that $f^{\prime}(3) = 2$, we have: $f^{\prime}(-3) = 2$.

If $f(x)$ is an odd differentiable function defined on $(-\infty, \infty)$ such that $f^{\prime}(3)=2,$ then $f^{\prime}(-3)$ is equal to

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