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

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

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

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

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

cos (x) + e^{- x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= cos (x) - (- e^{- x})

Simplify

= cos (x) + e^{- x}

\int θ cos (π) θ d θ

x \to 0 lim (x ln (2 x))

\int \frac{11 x ^{3}}{1 + x ^{2}} d x

\int \frac{2 r + 1}{r ^{2} - 3 r + 2} d r

\int - 3 ∣ x ∣ d x

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