MHT CET · Maths · Differentiation
If \(f(x)=e^{x} g(x), g(0)=4, g^{\prime}(0)=2\), then \(f^{\prime}(0)=\)
- A 4
- B 6
- C 1
- D 2
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
Given \(f(x)=e^{x} g(x)\)
\(\therefore f^{\prime}(x) =e^{x} g^{\prime}(x)+g(x) \cdot e^{x} \)
\( \therefore f^{\prime}(0) =e^{0} g^{\prime}(0)+g(0) \cdot e^{0} \)
\( =2+4=6\)
\(\therefore f^{\prime}(x) =e^{x} g^{\prime}(x)+g(x) \cdot e^{x} \)
\( \therefore f^{\prime}(0) =e^{0} g^{\prime}(0)+g(0) \cdot e^{0} \)
\( =2+4=6\)
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