Find derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): `(4x+5sinx)/(3x+7cosx)`

Explanation

To find the derivative of the function \( f(x) = \frac{4x + 5\sin x}{3x + 7\cos x} \), we will use the quotient rule. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then its derivative is given by:

\[ f'(x) = \frac{u'v - uv'}{v^2} \]

where \( u \) and \( v \) are functions of \( x \), and \( u' \) and \( v' \) are their respective derivatives.

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