Methods of Differentiations questions
285 published questions with worked solutions.
- Let y(x) = (1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^ 16 ). Then y' – y'' at x = –1 is equal to :
- Let y = f(x) = ^3 ( 3 ( 3 2 (-4x^3+5x^2+1)^ 3/2 ) ) Then at x = 1,
- Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and _ t x t^2f(x) - x^2f(t) t - x = 1 for each x > 0. Then...
- If the function f(x) = x^3 + e^ x 2 and g(x) = f^ -1 (x), then the value of g′(1) is
- Let f(x) = 4 and f'(x) = 4. Then _ x 2 xf(2) - 2f(x) x - 2 is given by
- If f(x + y) = f(x) f(y) x y and f(5) = 2, f'(0) = 3 then f'(5) is
- If y = (x + 1 + x^2 )^n, then (1 + x^2 ) d^2y dx^2 + x dy dx is
- If f(x) = x^n, then the value of f(1) - f'(1) 1 + f''(1) 2! - f'''(1) 3! + (-1)^nf^n(1) n! is
- If x = e^ y + e^ y + , x > 0, then dy dx is
- Suppose f(x) is differentiable x = 1 and _ h 0 1 h f(1 + h) = 5, then f'(1) equals
- If x^m y^n = (x + y)^ m+n , then dy dx is
- Let y be an implicit function of x defined by x^ 2x - 2x^x y - 1 = 0. Then y'(1) equals
- If f(x)= _ x^2 ( _e x), then f'(x) at x=e is
- If f(x)= ^ -1 ( 2.3^x 1+9^x ), then f' ( 12 ) equals
- If y= [e^ 4x ( x-4 x+3 )^ 3 4 ], then dy dx =
- If y= 1- ^ -1 x 1+ ^ -1 x then ( dy dx ) at x=0 is
- If y = [(x+1)(2x+1)(3x+1) (nx+1) ]^4, then dy dx at x = 0 is
- If y= [e^ 5x ( 3x-4 x+5 )^ 43 ], then dy dx is equal to
- If f(x) = ^ -1 x, g(x) = e^x and h(x) = g(f(x)), then h'(x) h(x) =
- If y= ((x+1)(4x+1)(9x+1) (n^2x+1) )^2 then dy dx at x=0 is
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