KCET · Maths · Inverse Trigonometric Functions
If \( y=f\left(x^{2}+2\right) \) and \( f^{\prime}(3)=5 . \) then \( \frac{d y}{d x} \) at \( x=1 \) is
- A \( 05 \)
- B (15)
- C \( 15 \)
- D \( 10 \)
Answer & Solution
Correct Answer
(D) \( 10 \)
Step-by-step Solution
Detailed explanation
Given that, \(y=\mathrm{f}\left(x^{2}+2\right) \rightarrow(1)\)
and \(\mathrm{f}^{\prime}(3)=5 \rightarrow(2)\)
Now, \(\frac{d y}{d x}=\mathrm{f}^{\prime}\left(x^{2}+2\right)(2 x)\)
At \(x=1\), we get \(\left.\cdot \frac{d y}{d x}\right|_{x}=1=f^{\prime}(1+2)(2)=2 f(3)\)
\(=2(5)=10\)
and \(\mathrm{f}^{\prime}(3)=5 \rightarrow(2)\)
Now, \(\frac{d y}{d x}=\mathrm{f}^{\prime}\left(x^{2}+2\right)(2 x)\)
At \(x=1\), we get \(\left.\cdot \frac{d y}{d x}\right|_{x}=1=f^{\prime}(1+2)(2)=2 f(3)\)
\(=2(5)=10\)
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