Exams › JEE Main › Maths

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:

1. 4e
2. 2e²
3. 4e²
4. 2e

Correct answer: 4e

Solution

The derivative of h(x) can be found using the chain rule, where h'(x) = f'(f(x)) * f'(x). Given that f'(x) = f(x), we can substitute to find h'(1) = f'(f(1)) * f'(1) = f(2) * f(1). Since f(1) = 2 and f(2) = e² (from the differential equation), we get h'(1) = e² * 2 = 4e.

Related JEE Main Maths questions

• Suppose f(x)=α(x)β(x)γ(x) for every real x, where α(x), β(x), and γ(x) are differentiable. If f'(2)=18f(2), α'(2)=3α(2), β'(2)=-4β(2), and γ'(2)=kγ(2), then what is the value of k?
• For the piecewise-defined function f(x) = { [sin((a+1)x) + sin x]/x, x < 0; c, x = 0; [√(x + bx²) - √x]/(b x^(3/2)), x > 0 } to be continuous at x = 0, which values of a, b, and c are required?
• Let f(x) and g(x) be continuously differentiable functions such that f'(x) = g(x) and f''(x) = -f(x). Define h(x) = [f(x)]² + [g(x)]². If h(0) = 5, what is the value of h(10)?
• For what value of p can the function f(x) = { ((4^x - 1)³)/(sin x · [log|1 + x²/3|]^p), x ≠ 0; 12(log 4)³, x = 0 } be made continuous at x = 0?
• Consider the function f: R -> R given by f(x) = max{x, x³}. At which points is f(x) not differentiable?
• Consider the function f(x)=[(1-sin³ x)/(3cos² x),, x<(π)/(2),; [4pt] p,, x=(π)/(2),; [4pt] q(1-sin x),, x>(π)/(2).] If f is continuous at x=(π)/(2), then the pair (p,q) is

⚔️ Practice JEE Main Maths free + battle 1v1 →