calculate derivative y =5x^6+ln (sin x)

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You need to differentiate the function with respect to x, such that:

`(dy)/(dx) = 5*(d(x^6))/(dx) + (d(ln(sin x)))/(dx)`

`(dy)/(dx) = 5*6*x^5 + 1/(sin x)*(d(sin x))/(dx)`

`(dy)/(dx) = 30x^5 + cos x/sin x`

Replacing the quotient `cos x/sin x` by the function `cot x` yields:

`(dy)/(dx) = 30x^5 + cot x`

Hence, evaluating the derivative of the given function, using the rules of differentiation, yields `(dy)/(dx) = 30x^5 + cot x` .