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

The derivative of y=sin(e^x) is cos(e^x)e^x

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

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

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derivative of

y = sin (e^{x})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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