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Alyce Wilkinson

Answered question

2021-10-12

Derivatives involving other trigonometric functions Find the derivative of the following functions.

y = \csc^{2} θ - 1

Answer & Explanation

un4t5o4v

Skilled2021-10-13Added 105 answers

Step 1
To differentiate:

y = \csc^{2} θ - 1

Solution:

y = \csc^{2} θ - 1

Differentiating both sides w.r.t

θ

we get:

\frac{d y}{d θ} = \frac{d}{d θ} (\csc^{2} θ - 1)

\Rightarrow \frac{d y}{d θ} = (2 \csc θ) \cdot \frac{d}{d θ} (\csc θ) - 0

(using,

\frac{d}{d x} (f (g (x)) = f^{'} (g (x)) \cdot g^{'} (x))

)

\Rightarrow \frac{d y}{d θ} = (2 \csc θ) (- \csc θ \cot θ)

(using,

\frac{d}{d x} (\csc x) - \cot x \csc x

)

\Rightarrow \frac{d y}{d θ} = - 2 \csc^{2} θ \cot θ

Step 2
Result:

\frac{d y}{d θ} = - 2 \csc^{2} θ \cot θ

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