Derivatives of Functions: JEE Questions & Solutions

Let f(x) = x³ + x² f'(1) + 2x f''(2) + f'''(3), x ∈ ℝ. Then the value of f'(5) is:

Let f: ℝ → ℝ be a twice differentiable function such that (sin x cos y)(f(2x + 2y) - f(2x - 2y)) = (cos x sin y)(f(2x + 2y) + f(2x - 2y))…

Let f be a differentiable function on ℝ such that f(2) = 1 and f'(2) = 4. Let lim_(x → 0) ( f(2+x))^(3/x) = e^α. Then the number of times…

Given f(x) = x³ + x² f'(1) + x f''(2) + f'''(3), x ∈ ℝ. Then f'(10) is equal to:

Let g(x) = 3f(x/3) + f(3 - x) where f''(x) > 0 for all x ∈ (0,3). If g is decreasing in (0, α) and increasing in (α,3), what is 8α?

Suppose f(x) = (2^x + 2^(-x))tan x √tan⁻¹(x² - x + 1)/(7x² + 3x + 1)³. The value of f'(0) is equal to:

Let f(x) = 2^x - x², x ∈ R. If m and n are respectively the number of points at which the curves y = f(x) and y = f'(x) intersect the…

Let y = ln((1 - x²)/(1 + x²)), -1 < x < 1. Then at x = 1/2, the value of 225(y' - y'') is equal to:

If f(x) = x³ - x² f'(1) + x f''(2) - f'''(3), x ∈ ℝ, then:

If 2x^y + 3y^x = 20, then dy/dx at (2,2) is equal to: