Sum

if `y = tan^2(log x^3)`, find `(dy)/(dx)`

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#### 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)`

Concept: Derivatives of Composite Functions - Chain Rule

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