What is the derivative of sin(e^{5x}) ?

The derivative of sin(e^{5x}) is cos(e^{5x})e^{5x}*5

What is the first derivative of sin(e^{5x}) ?

The first derivative of sin(e^{5x}) is cos(e^{5x})e^{5x}*5

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\frac{d}{d x} (sin (e^{5 x}))

cos (e^{5 x}) e^{5 x} \cdot 5

Solution steps

\frac{d}{d x} (sin (e^{5 x}))

Apply the chain rule:

cos (e^{5 x}) \frac{d}{d x} (e^{5 x})

= cos (e^{5 x}) \frac{d}{d x} (e^{5 x})

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= cos (e^{5 x}) e^{5 x} \cdot 5

What is the derivative of sin(e^{5x}) ?
The derivative of sin(e^{5x}) is cos(e^{5x})e^{5x}*5
What is the first derivative of sin(e^{5x}) ?
The first derivative of sin(e^{5x}) is cos(e^{5x})e^{5x}*5