What is the derivative of cos(sin(e^x)) ?

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

What is the first derivative of cos(sin(e^x)) ?

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

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derivative of

cos (sin (e^{x}))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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

t (\frac{d y}{d t}) + 5 y = 4 t, y (1) = 2

x^{- \frac{3}{2}}

x \to + 5 lim (x^{2} - 2 x + 1)

\int \frac{2 + e ^{x}}{2 - e ^{x}} d x

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