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Popular >

derivative of 1-e^{-x}sin(y)

Solution

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

Solution

- 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)

Popular Examples

derivative of sqrt(x/(x^2+5))

\frac{d}{d x} (\frac{x}{x ^{2} + 5})

(\partial)/(\partial x)(1/(sqrt(x)))

\frac{\partial}{\partial x} (\frac{1}{x})

area x^2=y^3,x=3y area

x^{2} = y^{3}, x = 3 y

inverse oflaplace 1/((s-1)(s^2+9))inverse laplace

\frac{1}{( s - 1 ) ( s ^{2} + 9 )}

integral of arctan(5x)

\int arctan (5 x) d x

Frequently Asked Questions (FAQ)

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)