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Question
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Solution 1
`y = [tan(3logx)]^2`
differentiate w.r.t. x both side
`:. (dy)/(dx) = 2[tan(3logx)] xx sec^2(3log x). 3/x`
`:. (dy)/(dx) =6/x tan(log x^3). sec^2 (log x^3)`
Solution 2
Given `y = tan^2(logx^3)`
We need to find `(dy)/(dx)`
Consider `y = tan^2(logx^3)`
⇒ `y = tan^2(3 logx)`
⇒ `y = [tan(3logx)]^2`
Differentiate with respect to x on both sides we get
⇒ `dy/dx = 2[tan(3logx)] . sec^2(3logx) . 3/x`
⇒ `dy/dx = 6/x . [tan(3logx)] . sec^2(3 logx)`
`therefore dy/dx = 6/x . [tan(logx^3)] . sec^2(logx^3)`
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