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Home » Find the derivative of the following functions (it is to be understood that  and  are fixed non-zero constants and  and  are integers) : .
Find the 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) : \frac{{{x^2}\cos \left( {\frac{\pi }{4}} \right)}}{{\sin x}}.
CBSE | Class 11 | Limits and Derivatives | Maths | Miscellaneous Exercise | NCERT
Find the 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) : \frac{{{x^2}\cos \left( {\frac{\pi }{4}} \right)}}{{\sin x}}.

Assume, f(x) = \frac{{{x^2}\cos \left( {\frac{\pi }{4}} \right)}}{{\sin x}}.

Upon differentiating with respect to x and applying quotient rule we get,

{f^\prime }(x) = \cos \frac{\pi }{4} \cdot \left[ {\frac{{\sin x\frac{d}{{dx}}\left( {{x^2}} \right) - {x^2}\frac{d}{{dx}}(\sin x)}}{{{{\sin }^2}x}}} \right]

f'(x) = \cos \frac{\pi }{4} \cdot \left[ {\frac{{\sin x \cdot 2x - {x^2}\cos x}}{{{{\sin }^2}x}}} \right]

Therefore, f'(x) = \frac{{x\cos \frac{\pi }{4}[2\sin x - x\cos x]}}{{{{\sin }^2}x}}.

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