AP EAMCET · Maths · Differentiation
If \(y=(\tan x)^{\sin x}\), then \(\frac{d y}{d x}\) is equal to
- A \((\tan x)^{\sin x}\{\sec x+(\cos x)(\log (\tan x))\}\)
- B \((\sin x)^{\tan x}\{\sec x+(\cos x)(\log (\tan x))\}\)
- C \((\tan x)^{\sin x}\{\sec x-(\cos x)(\log (\tan x))\}\)
- D \((\sin x)^{\tan x}\{\sec x-(\cos x)(\log (\tan x))\}\)
Answer & Solution
Correct Answer
(A) \((\tan x)^{\sin x}\{\sec x+(\cos x)(\log (\tan x))\}\)
Step-by-step Solution
Detailed explanation
We have, \(y=(\tan x)^{\sin x} \Rightarrow y=e^{\sin x \log \tan x}\) \(\frac{d y}{d x}=e^{\sin x \log \tan x}\left(\frac{\sin x}{\tan x} \sec ^2 x+\cos x \log \tan x\right)\) \(\Rightarrow \frac{d y}{d x}=(\tan x)^{\sin x}(\sec x+\cos x \log \tan x)\)
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