Tricky differentiatio
Calculus
Level
pending
If f(x) is an odd differentiable function defined on (-∞,∞) such that , then is
2
-2
1
4
0
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1 solution
Well I'll prove that derivative of every odd function is an even function. Then the answer is obvious.
For an odd function:- f ( x ) + f ( − x ) = 0 Now differentiating both sides:- f ′ ( x ) − f ′ ( − x ) = 0 ⟹ f ′ ( x ) = f ′ ( − x ) Hence f ′ ( x ) is an even function. So f ′ ( − 3 ) = 2