Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Calculus question (Derivative)?

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

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  • Vaman
    Lv 7
    1 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.

  • rotchm
    Lv 7
    1 month ago

    Hint: Whats the derivative of a^(f(x)) ? 

    Unanon yourself and I will detail further. 

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