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What is derivative of y = 2^(sin x)+3^(cos x)?

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ruals | Salutatorian

Posted September 22, 2013 at 5:10 PM via web

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What is derivative of y = 2^(sin x)+3^(cos x)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 22, 2013 at 5:40 PM (Answer #1)

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You need to differentiate the function with respect to `x` , using the chain rule, such that:

`y' = (2^(sin x))' + (3^(cos x))'`

`y' = 2^(sin x)*ln 2*(sin x)' + 3^(cos x)*ln 3*(cos x)'`

`y' = 2^(sin x)*ln 2*cos x + 3^(cos x)*ln 3*(- sin x)`

`y' = 2^(sin x)*ln 2*cos x - 3^(cos x)*ln 3*sin x`

Hence, evaluating the derivative of the given function, using the chain rule, yields `y' = 2^(sin x)*ln 2*cos x - 3^(cos x)*ln 3*sin x.`

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