What is the derivative of sin(e^{3x}) ?

The derivative of sin(e^{3x}) is cos(e^{3x})e^{3x}*3

What is the first derivative of sin(e^{3x}) ?

The first derivative of sin(e^{3x}) is cos(e^{3x})e^{3x}*3

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\frac{d}{d x} (sin (e^{3 x}))

cos (e^{3 x}) e^{3 x} \cdot 3

Solution steps

\frac{d}{d x} (sin (e^{3 x}))

Apply the chain rule:

cos (e^{3 x}) \frac{d}{d x} (e^{3 x})

= cos (e^{3 x}) \frac{d}{d x} (e^{3 x})

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= cos (e^{3 x}) e^{3 x} \cdot 3

\frac{1}{3 ^{x}}

f (x) = \frac{x ^{2} - 1}{2 x + 2}

f (x) = 4 x^{4} - 5 x^{3} + 2 x - 3

\frac{d}{d x} (\frac{x}{a ^{2} a ^{2} + x ^{2}})

What is the derivative of sin(e^{3x}) ?
The derivative of sin(e^{3x}) is cos(e^{3x})e^{3x}*3
What is the first derivative of sin(e^{3x}) ?
The first derivative of sin(e^{3x}) is cos(e^{3x})e^{3x}*3