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Let f(x) = x – [x], then f ‘ (x) = 1 for
f(x) = x [x] is derivable at all x ∈ R – I , and f ‘(x) = 1 for all x ∈ R – I .
f (x) = max {x, x^{3}},then the number of points where f (x) is not differentiable, are
f(x)=m{x,x^{3}}
= x;x<−1 and
= x^{3};−1≤x≤0
⇒ f(x)=x;0≤x≤1 and
= x^{3};x≥1
∴ f(x)=1;x<−1
∴ f′(x)=3x^{2};− 1≤x≤0 and =1
0<x<1
Hence answer is 3
f(x) = 1+sinx is not derivable at those x for which sinx = 0, however, 1+sinx is continuous everywhere (being the sum of two continuous functions)
Let f (x + y) = f(x) + f(y) ∀ x, y ∈ R. Suppose that f (6) = 5 and f ‘ (0) = 1, then f ‘ (6) is equal to
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d/dx(logx)
= 1/x
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If x sin (a + y) = sin y, then is equal to
x sin(a+y) = sin y
⇒
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Let f be a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈ R, then f ‘ (x) =
If x = at^{2}, y = 2at, then is equal to
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