Question

Q. 1) If y = 2^(log(cos x)) then find the value of dy/dx.

Q. 2) If y = log_7(log_7 x) then find dy/dx.

Refer attachments .
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Answer 1

Step-by-step explanation:

1. Use chain rule

$\frac{dy}{dx} = \frac{d}{dx} ( log_{7}( log_{7}(x) ) \\ \\ = \frac{1}{ log(7) .log_{7}(x) } \frac{d}{dx} ( log_{7}(x) ) \\ \\ = \frac{1}{ log(7) \frac{ log(x) }{ log(7) } } . \frac{1}{x log(7) } \\ \\ = \frac{1}{x log(x) log(7) }$

2.

$\frac{d}{dx} {2}^{ log( \cos(x) ) } \\ \\ = {2}^{ log( \cos(x) ) }log(2) \frac{d}{dx} ( log( \cos(x) ) \\ \\ = {2}^{ log( \cos(x) ) } log(2). \frac{1}{ \cos(x) } \frac{d}{dx} ( \cos(x)) \\ \\ = {2}^{ log( \cos(x) ) } log(2)( \frac{ - \sin(x) }{ \cos(x) } )\\ \\ = - \log(2) \tan(x) {2}^{ log( \cos(x) ) }$

Answer 2

Step-by-step explanation:

given :

If y = 2^(log(cos x)) then find the value of dy/dx.

to find :

find the value of dy/dx.

solution :

• ans 1. Let y = log(cos ex)

• By using the chain rule, we obtain

• ""dy"/"dx" = "d"/"dx"["log" (cos"e"^"x")]

• `= 1/cos"e"^"x" . "d"/"dx"(cos"e"^"x")`

• = 1/(cos"e"^"x"). (-sin"e"^"x"). "d"/"dx"

• ("e"^"x")"

• = (-sin"e"^"x")/(cos"e"^"x"). "e"^"x"

• =-"e"^"x" tan"e"^"x", "e"^"x" # (2"n"+1)pi/2, "n"E "N"

• answer 2 in attachment please check