What is the derivative of 1-e^{-x}sin(y) ?

The derivative of 1-e^{-x}sin(y) is -e^{-x}cos(y)(dy)/(dx)+e^{-x}sin(y)

What is the first derivative of 1-e^{-x}sin(y) ?

The first derivative of 1-e^{-x}sin(y) is -e^{-x}cos(y)(dy)/(dx)+e^{-x}sin(y)

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\frac{d}{d x} (1 - e^{- x} sin (y))

- e^{- x} cos (y) \frac{d y}{d x} + e^{- x} sin (y)

Solution steps

\frac{d}{d x} (1 - e^{- x} sin (y))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (e^{- x} sin (y))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (e^{- x} sin (y)) = - e^{- x} sin (y) + e^{- x} cos (y) \frac{d y}{d x}

= 0 - (- e^{- x} sin (y) + e^{- x} cos (y) \frac{d y}{d x})

Simplify

= - e^{- x} cos (y) \frac{d y}{d x} + e^{- x} sin (y)

What is the derivative of 1-e^{-x}sin(y) ?
The derivative of 1-e^{-x}sin(y) is -e^{-x}cos(y)(dy)/(dx)+e^{-x}sin(y)
What is the first derivative of 1-e^{-x}sin(y) ?
The first derivative of 1-e^{-x}sin(y) is -e^{-x}cos(y)(dy)/(dx)+e^{-x}sin(y)