What is the derivative of sin(xe^{-cos(x)}) ?

The derivative of sin(xe^{-cos(x)}) is e^{-cos(x)}cos(x)+e^{-cos(x)}sin^2(x)

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

The first derivative of sin(xe^{-cos(x)}) is e^{-cos(x)}cos(x)+e^{-cos(x)}sin^2(x)

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\frac{d}{d x} (sin (x) e^{- c o s (x)})

e^{- c o s (x)} cos (x) + e^{- c o s (x)} sin^{2} (x)

Solution steps

\frac{d}{d x} (sin (x) e^{- c o s (x)})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = e^{- c o s (x)}

= \frac{d}{d x} (sin (x)) e^{- c o s (x)} + \frac{d}{d x} (e^{- c o s (x)}) sin (x)

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

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

= cos (x) e^{- c o s (x)} + e^{- c o s (x)} sin (x) sin (x)

e^{- c o s (x)} sin (x) sin (x) = e^{- c o s (x)} sin^{2} (x)

= e^{- c o s (x)} cos (x) + e^{- c o s (x)} sin^{2} (x)

x \to 100000 lim (x^{3} + 2 x + 1)

\frac{d}{d x} (2 x^{2} - 2 x + c)

\frac{d ^{2}}{d x ^{2}} (x (2 x + 1)^{5})

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

y^{^{'}} + (tan (x)) y = cos (x)

What is the derivative of sin(xe^{-cos(x)}) ?
The derivative of sin(xe^{-cos(x)}) is e^{-cos(x)}cos(x)+e^{-cos(x)}sin^2(x)
What is the first derivative of sin(xe^{-cos(x)}) ?
The first derivative of sin(xe^{-cos(x)}) is e^{-cos(x)}cos(x)+e^{-cos(x)}sin^2(x)