What is the derivative of cos(e^{-θ^2}) ?

The derivative of cos(e^{-θ^2}) is 2e^{-θ^2}θsin(e^{-θ^2})

What is the first derivative of cos(e^{-θ^2}) ?

The first derivative of cos(e^{-θ^2}) is 2e^{-θ^2}θsin(e^{-θ^2})

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derivative of

cos (e^{- θ^{2}})

2 e^{- θ^{2}} θ sin (e^{- θ^{2}})

Solution steps

\frac{d}{d θ} (cos (e^{- θ^{2}}))

Apply the chain rule:

- sin (e^{- θ^{2}}) \frac{d}{d θ} (e^{- θ^{2}})

= - sin (e^{- θ^{2}}) \frac{d}{d θ} (e^{- θ^{2}})

\frac{d}{d θ} (e^{- θ^{2}}) = - 2 e^{- θ^{2}} θ

= - sin (e^{- θ^{2}}) (- 2 e^{- θ^{2}} θ)

Simplify

= 2 e^{- θ^{2}} θ sin (e^{- θ^{2}})

\int (- 9) d x

\int_{- 3}^{3} x^{- \frac{1}{3}} d x

\int_{- 1}^{2} x + 2 - x^{2} d x

x \to π lim ((x - π) csc (x))

e^{x} \frac{y d y}{d x} = e^{- y} + e^{- 2 x - y}

What is the derivative of cos(e^{-θ^2}) ?
The derivative of cos(e^{-θ^2}) is 2e^{-θ^2}θsin(e^{-θ^2})
What is the first derivative of cos(e^{-θ^2}) ?
The first derivative of cos(e^{-θ^2}) is 2e^{-θ^2}θsin(e^{-θ^2})