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

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

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

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

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\frac{d}{d x} (e^{- (c o s (x) + s i n (y))})

e^{- c o s (x) - s i n (y)} (sin (x) - cos (y) \frac{d y}{d x})

Solution steps

\frac{d}{d x} (e^{- (c o s (x) + s i n (y))})

Simplify

e^{- (c o s (x) + s i n (y))} : e^{- c o s (x) - s i n (y)}

= \frac{d}{d x} (e^{- c o s (x) - s i n (y)})

Apply the chain rule:

e^{- c o s (x) - s i n (y)} \frac{d}{d x} (- cos (x) - sin (y))

= e^{- c o s (x) - s i n (y)} \frac{d}{d x} (- cos (x) - sin (y))

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

= e^{- c o s (x) - s i n (y)} (sin (x) - cos (y) \frac{d y}{d x})

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{5 + 4 x})

\int (5 x) d x

\int (1 - cos (x))^{3} sin (x) d x

\int x 4 - x^{2} d x

\frac{\partial}{\partial x} (\frac{a}{a - x})

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