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

The derivative of x*e^{-sin(x}-x) is e^{-sin(x)}-e^{-sin(x)}xcos(x)-1

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

The first derivative of x*e^{-sin(x}-x) is e^{-sin(x)}-e^{-sin(x)}xcos(x)-1

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\frac{d}{d x} (x \cdot e^{- s i n (x)} - x)

e^{- s i n (x)} - e^{- s i n (x)} x cos (x) - 1

Solution steps

\frac{d}{d x} (x e^{- s i n (x)} - x)

Apply the Sum/Difference Rule:

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

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

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

\frac{d x}{d x} = 1

= e^{- s i n (x)} - e^{- s i n (x)} x cos (x) - 1

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