What is the derivative of $f (x) = \frac{cos x}{csc x}$ $f(x)=cosx/cscx$ ?

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What is the derivative of $f (x) = \frac{cos x}{csc x}$ $f(x)=cosx/cscx$ ?

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Answer 1 · 2015-10-30T10:51:32

$\frac{d}{d x} (\frac{cos x}{cos e c x}) = \frac{- sin x \cdot cos e c x + cos x \cdot cos e c x \cdot cot x}{cos e c^{2} x}$ $d/dx (cosx/(cosecx))=(-sinx*cosecx+cosx*cosecx*cotx)/(cosec^2x)$

Explanation:

Application of the quotient rule for differentiation yields

$\frac{d}{d x} (\frac{cos x}{cos e c x}) = \frac{- sin x \cdot cos e c x + cos x \cdot cos e c x \cdot cot x}{cos e c^{2} x}$ $d/dx (cosx/(cosecx))=(-sinx*cosecx+cosx*cosecx*cotx)/(cosec^2x)$

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What is the derivative of $f (x) = \frac{cos x}{csc x}$ $f(x)=cosx/cscx$ ?

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What is the derivative of $f (x) = \frac{cos x}{csc x}$ $f(x)=cosx/cscx$ ?