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Math Help - differentiontion of hyperbolic trigonometry function

  1. #1
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    differentiontion of hyperbolic trigonometry function

    is it use same method to do differentiation between hyperbolic trigo and normaal trigo?

    if the question ask d/dx(4sinh^5 3x) after i differentiate it, is the answer become 60 sinh^4 3x?
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  2. #2
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    Quote Originally Posted by emperror123 View Post
    is it use same method to do differentiation between hyperbolic trigo and normaal trigo?

    if the question ask d/dx(4sinh^5 3x) after i differentiate it, is the answer become 60 sinh^4 3x?
    I suspect your text book will tell you that the derivative of sin(x) is cos(x), the derivative of cos(x) is -sin(x), the derivative of sinh(x) is cosh(x), and the derivative of cosh(x) is sinh(x).
    No, the derivative of 4 sinh^5(3x) is NOT 60 sinh^4(3x). Nor is the derivative of 4 sin^5(3x) equal to 60 sin^4(3x).

    The derivative of 4sin^5(3x) is 4(5)(sin^4(3x) times the derivative of sin(3x) which is 3 cos(3x). That is, the derivative of 4sin^5(3x) is 60sin^4(3x)cos(3x).

    Now, back to you- what is the derivative of 4 sinh^5(3x)? What is the derivative of 4 cosh^5(3x)?
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  3. #3
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    derivation of 4 sinh^5 3x = 60sinh^4 3x cosh 3x
    derivation of 4 cosh^5 3x = 60 cosh^4 3x sinh 3x
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