"Find the derivatives of the following functions. f(x)=sin⁡hx1+sin⁡hx" was answered by students like you

Alyce Wilkinson

Answered question

2021-03-29

Find the derivatives of the following functions.

f (x) = \frac{\sin h x}{1 + \sin h x}

Answer & Explanation

likvau

Skilled2021-03-31Added 75 answers

Step 1
Given:

\Rightarrow f (x) = \frac{\sin h x}{1 + \sin h x}

Step 2

\Rightarrow f (x) = \frac{\sin h x}{1 + \sin h x}

Differentiating both the sides with respect to x:

\Rightarrow \frac{d f (x)}{d x} = \frac{d}{d x} (\frac{\sin h x}{1 + \sin h x})

\Rightarrow \frac{d f (x)}{d x} = \frac{(1 + \sin h x) \cos h x - \sin h x \cos h x}{{(1 + \sin h x)}^{2}}

\Rightarrow \frac{d f (x)}{d x} = \frac{\cos h x + \sin h \cos h x - \sin h x \cos h x}{{(1 + \sin h x)}^{2}}

\Rightarrow \frac{d f (x)}{d x} = \frac{\cos h x}{{(1 + \sin h x)}^{2}}

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