Methods of Differentiations questions
285 published questions with worked solutions.
- If y = ( ^ -1 x), then dy dx at x = 1 is equal to -
- Let f(x) = x^3 + x^2 f'(1) + 2xf''(2) + f'''(3), x R. Then the value of f'(5) is:
- Let y=y(x) be a differentiable function in the interval (0, ) such that y(1)=2. and _ t x ( t^2y(x)-x^2y(t) x-t ) = 3 for each...
- Let f : R → R be a twice differentiable function such that ( x y)(f(2x+2y)-f(2x-2y)) = ( x y)(f(2x+2y)+f(2x-2y)), for all x, y ∈...
- Let f be a real-valued function defined on the interval (-1,1) such that e^ -x f(x)=2+ _0^x t^4+1 ,dt, and let f^ -1 be the...
- If g is the inverse of a function f and f'(x) = 1 1 + x^5 , then g'(x) is equal to:
- If x = 2^ cosec ^ -1 t and y = 2^ ^ -1 t (|t| 1), then dy dx is equal to -
- If f(1) = 1, f′(1) = 3, then the derivative of f(f(f(x))) + (f(x))^2 at x = 1 is:
- If x^2 + y^2 + y = 4, then the value of d^2y dx^2 at the point (–2, 0) is
- If f(x) = ^ -1 ( 2 3^x 1 + 9^x ), then f' (- 1 2 ) equals
- If x = 3 tan t and y = 3 sec t, then the value of d^2y dx^2 at t = 4, is:
- If e^y + xy = e, the ordered pair ( dy dx , d^2y dx^2 ) at x = 0 is equal to:
- Let f be a differentiable function such that f(1) = 2 and f′(x) = f(x) for all x ∈ R. If h(x) = f(f(x)), then h′(1) is equal to:
- For x > 1, if (2x)^ 2y = 4e^ 2x-2y , then (1 + _e2x)^2 dy dx is equal to:
- If x _e( _ex) - x^2 + y^2 = 4 (y > 0), then dy dx at x = e is equal to:
- The derivative of ^ -1 ( x - x x + x ), with respect to x2, where x (0, 2 ) is:
- Let y = y(x) be a function of x satisfying y 1-x^2 =k-x 1-y^2 where k is a constant and y ( 1 2 )=- 1 4 . Then dy dx at x= 1 2 ,...
- If x=2 - 2 and y=2 - 2 , [0,2 ], then d^2y dx^2 at = is -
- Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b R, g'(a) = 5 and g(a) = b,...
- If y = ( x + 1)(x^2 - x) x x + x + x + 1 15 (3 ^2x - 5) ^3x, then 96 ,y' ( 6 ) is equal to ______.
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