How do you differentiate f(x)=csc(sqrt(x^2-5x)) f(x)=csc(√x2−5x) using the chain rule?

1 Answer
Deepak Pandey · Monzur R.
Aug 25, 2017

f'(x)=-(2x-5)/(2sqrt (x^2-5x))csc (sqrt (x^2-5x))cot (sqrt (x^2-5x))

Explanation:

f (x)=csc(sqrt (x^2-5x))
Differentiating both sides with respect to x we get
f'(x)=-csc (sqrt (x^2-5x)).cot (sqrt (x^2-5x))×d/dx (sqrt (x^2-5x))
=>f'(x)=-csc (sqrt (x^2-5x)).cot (sqrt (x^2-5x))×1/(2sqrt (x^2-5x))×(2x-5)
:.f'(x)=-(2x-5)/(2sqrt (x^2-5x))csc (sqrt (x^2-5x))cot (sqrt (x^2-5x))

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