Methods of Differentiations questions
285 published questions with worked solutions.
- Let f(x) = x⁵ + 2e^ x/4 for all x ∈ R. Consider a function g(x) such that (gof)(x) = x for all x ∈ R. Then the value of 8g′(2) is:
- Let f(x) = x⁵ + 2x³ + 3x + 1, x ∈ R, and g(x) be a function such that g(f(x)) = x for all x ∈ R. Then g(7) g'(7) is equal to:
- Let f be a differentiable function in the interval (0, ∞) such that f(1) = 1 and _ t x t^2f(x) - x^2f(t) t - x = 1 for each x >...
- Suppose for a differentiable function h, h(0) = 0, h(1) = 1 and h′(0) = h′(1) = 2. If g(x) = h(eˣ)e^ h(x) , then g′(0) is equal...
- If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a > b > 0, then dx dy at ( 4 , 4 ) is :
- Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy^2 + x^2y. for all real x and y. If _ x...
- The derivative of ^ -1 ( 1+x^2 -1 x ) with respect to ^ -1 ( 2x 1-x^2 1-2x^2 ) at x = 1 2 is :
- If log_e y = 3 sin⁻¹x, then (1 − x²)y″ − xy′ at x = 1/2 is equal to :
- Let f(x) = x³ + x² f′(1) + x f″(2) + f‴(3), x ∈ R. Then f′(10) is equal to ______.
- Let y = _e ( 1 - x^2 1 + x^2 ), −1 < x < 1. Then at x = 1/2, the value of 225(y′ – y″) is equal to
- Suppose f(x) = (2^x + 2^ -x ) x ^ -1 (x^2 - x + 1) (7x^2 + 3x + 1)^3 . Then the value of f′(0) is equal to-
- If f(x) = vmatrix 2 ^4x & 2 ^4x & 3 + ^22x 3 + 2 ^4x & 2 ^4x & ^22x 2 ^4x & 3 + 2 ^4x & ^22x vmatrix , then 15f'(0) is equal to :
- If f(x) = vmatrix x^3 & 2x^2 + 1 & 1 + 3x 3x^2 + 2 & 2x & x^3 + 6 x^3 - x & 4 & x^2 - 2 vmatrix for all x ∈ ℝ, then 2f(0) + f′(0)...
- Let f : S S where S = (0, ) be a twice differentiable function such that f(x + 1) = xf(x). If g : S R be defined as g(x) =...
- If f(x) = ( ^ -1 ( 1-2^ 2x 1+2^ 2x ) ) and its first derivative with respect to x is - b a _e2 when x = 1, where a and b are...
- Let f : R R satisfy the equation f(x + y) = f(x). f(y) for all x, y R and f(x) 0 for any x R. If the function f is differentiable...
- If y(x)= ^ -1 ( 1+ x + 1- x 1+ x - 1- x ), x ( 2 , ) then dy dx at x = 5 6 is :
- If y = y(x) is an implicit function of x such that _e(x+y)=4xy. then d^2y dx^2 at x = 0 is equal to _________.
- The value of _ h 0 2 3 ( 6 +h )- ( 6 +h ) 3h( 3 - ) is
- Let f : ℝ ℝ be defined as f(x) = x^ 3 + x - 5. If g(x) is a function such that f(g(x)) = x, ∀ 'x' ℝ, then g'(63) is equal to...
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