What is (\partial)/(\partial s)(-cos(s-t)) ?

The answer to (\partial)/(\partial s)(-cos(s-t)) is sin(s-t)

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(\partial)/(\partial s)(-cos(s-t))

\frac{\partial}{\partial s} (- cos (s - t))

sin (s - t)

Solution steps

\frac{\partial}{\partial s} (- cos (s - t))

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{\partial}{\partial s} (cos (s - t))

Apply the chain rule:

- sin (s - t) \frac{\partial}{\partial s} (s - t)

= - sin (s - t) \frac{\partial}{\partial s} (s - t)

\frac{\partial}{\partial s} (s - t) = 1

= - (- sin (s - t) \cdot 1)

Simplify

= sin (s - t)

What is (\partial)/(\partial s)(-cos(s-t)) ?
The answer to (\partial)/(\partial s)(-cos(s-t)) is sin(s-t)