TS EAMCET · Maths · Differentiation
If \(f\) is differentiable, \(f(x+y)=f(x) f(y)\) for all \(x, y \in \mathbb{R}, f(3)=3, f^{\prime}(0)=11\), then \(f^{\prime}(3)=\)
- A \(\frac{3}{11}\)
- B \(\frac{11}{3}\)
- C 8
- D 33
Answer & Solution
Correct Answer
(D) 33
Step-by-step Solution
Detailed explanation
We have, \(f(x+y)=f(x) f(y)\) differentiate with respect to \(x, y\) as constant, we get \[ f^{\prime}(x+y)=f^{\prime}(x) f(y) \] Put \(x=0, y=3\), we get…
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