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# Calculus question (Derivative)?

find the derivative of y=5^(1/x)+sin^2(cosx). All steps

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- VamanLv 71 month ago
Derivative of 5^(1/x). let z=5^(1/x), ln z= 1/x ln 5, Derivative is 1/z dz/dx= - ln5/x^2, dz/dx = z (-ln5/x^2)= -ln5 /x^2 5^(1/x)

sin^2 x= 1/2(1-cos 2x), sin^2 (cos x)= 1/2 (1-cos 2(cosx)).

derivative will be -1/2 sin 2( cos x)*2 sin x = -sin x sin (2 cos x). The derivative will be -ln5/x^2 5^(1/x) - sin x sin ( 2 cos x)

Please check the answer.

- rotchmLv 71 month ago
Hint: Whats the derivative of a^(f(x)) ?

Unanon yourself and I will detail further.

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