"Find the derivative of −sin⁡(x)" was answered by our experts

Stacie Worsley

Answered question

2021-12-14

Find the derivative of

- \sin (x)

Juan Spiller

Beginner2021-12-15Added 38 answers

f^{'} (x) = lim_{h \to 0} \frac{\sin (x + h) - \sin (x)}{h}

Let's use representation of a difference of sin functions as a product of sin and cos, and we get:

f^{'} (x) = lim_{h \to 0} \frac{2 \times \sin (\frac{h}{2}) \cos (x + \frac{h}{2})}{h}

f^{'} (x) = lim_{h \to 0} \frac{\sin (\frac{h}{2})}{\frac{h}{2}} \times lim_{h \to 0} \cos (x + \frac{h}{2})

f^{'} (x) = 1 \times \cos (x) = \cos (x)

Thus, the derivative is

f^{'} (x) = \cos (x)

Foreckije

Beginner2021-12-16Added 32 answers

\frac{d}{d x} (- \sin (x))

Take the constant out

- \frac{d}{d x} (\sin (x))

Apply the common derivative:

= - \cos (x)

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