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If y=(x)^(cosx)+(cosx)^(sinx), find (dy)...

If `y=(x)^(cosx)+(cosx)^(sinx)`, find `(dy)/(dx).`

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To find the derivative of the function \( y = x^{\cos x} + \cos^{\sin x} x \), we will use the properties of logarithmic differentiation and the chain rule. Here’s a step-by-step solution: ### Step 1: Define the function Let \[ y = x^{\cos x} + \cos^{\sin x} x \] ...
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y=(sinx)^(cosx)+(cosx)^(sinx)

If y=sin(cosx^(2)), find (dy)/(dx) .

Knowledge Check

  • If y=(cosx-sinx)/(cosx+sinx)," then "(d^(2)y)/(dx^(2)):(dy)/(dx)=

    A
    y
    B
    `-2y`
    C
    3y
    D
    `-4y`

  • If y=cosx^3 , then find (dy)/(dx) .

    A
    `3x^2sinx^3`
    B
    `-3x^2cosx^3`
    C
    `-3x^2sinx^2`
    D
    `-3x^2sinx^3`

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    If (cosx)^(y)=(siny)^(x), then find (dy)/(dx) .

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