Question

f(x) = e^3x + sin(x) what is f''(x)

Answer 1

\[\frac{ d }{ dx }e^{x} = e^{x} \times x' = e^{x}\]

Answer 2

\[\frac{ d }{ dx }\sin(x) = \cos(x)\]

Answer 3

\[\Large f(x) = e^{3x} + \sin(x)\]


\[\Large \frac{d}{dx}(f(x)) = \frac{d}{dx}(e^{3x} + \sin(x))\]


\[\Large \frac{d}{dx}(f(x)) = \frac{d}{dx}(e^{3x}) + \frac{d}{dx}(\sin(x))\]


\[\Large \frac{d}{dx}(f(x)) = 3e^{3x} + \cos(x)\]


\[\Large f^{\prime}(x) = 3e^{3x} + \cos(x)\]


\[\Large \frac{d}{dx}(f^{\prime}(x)) = \frac{d}{dx}(3e^{3x} + \cos(x))\]


\[\Large \frac{d}{dx}(f^{\prime}(x)) = \frac{d}{dx}(3e^{3x}) + \frac{d}{dx}(\cos(x))\]


\[\Large \frac{d}{dx}(f^{\prime}(x)) = 3*3e^{3x} - \sin(x)\]


\[\Large f^{\prime\prime}(x) = 9e^{3x} - \sin(x)\]

Answer 4

f'(x) = 3e^3x + cosx
f''(x) = 9e^3x - sinx

Answer 5

I'm using the idea that the derivative of e^x is e^x

also, d/dx[sin(x)] = cos(x) and d/dx[cos(x)] = -sin(x)