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

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

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

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

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

- sin (e^{3 x}) e^{3 x} \cdot 3

Solution steps

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

Apply the chain rule:

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

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

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

= - sin (e^{3 x}) e^{3 x} \cdot 3

\int_{1}^{5} 2 x + 1 d x

\frac{4 x ^{2} + 4 x + 2}{x}

\int \frac{( x ^{3} + x )}{1 - x ^{4} - x ^{2}} d x

x \to 2 lim (2 x^{2} - 4 x + 3)

\int \frac{e ^{y} sin ( 2 x )}{cos ( x )} d x

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