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The derivative of sin (x²) w.r.t. x, at x = √π is :
If f(x) = |tan 2x|, then find the value of f′(x) at x = π/3.
If x = e^(x/y), prove that dy/dx = (log x – 1)/(log x)²
Check the differentiability of f(x) = {x² + 1, 0 ≤ x < 1; 3 – x, 1 ≤ x ≤ 2} at x = 1.
Find the value of a and b so that function f defined as : f(x) = {(x – 2)/(|x – 2|) + a, if x < 2; a + b, if x = 2; (x – 2)/(|x – 2|) + b, if x > 2} is a continuous function.
Let f(x) = |x² sin x; p -1|, where p is a constant. The value of p for which f'(0) = 1 is :
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