Question

F(x) =sin6x-e³x+4найти f(x) ​

Answer 1

sin(6.x) - e.x + 4) = 6 cos(6.x) -
dx
(sin(6.x) - ex+4)

Answer 2

To find the derivative $f(x)$ of the given function $F(x) = \sin(6x) - e^{3x} + 4$, we'll use the chain rule and the derivatives of sine and exponential functions. Let's break it down step by step:

1. Derivative of $\sin(6x)$: The derivative of $\sin(ax)$ with respect to $x$ is $a\cos(ax)$. So, for $\sin(6x)$, the derivative is $6\cos(6x)$.

2. Derivative of $-e^{3x}$: The derivative of $e^{ax}$ with respect to $x$ is $ae^{ax}$. So, for $-e^{3x}$, the derivative is $-3e^{3x}$.

Putting it all together, the derivative of $F(x)$ with respect to $x$ is: $f(x) = \frac{d}{dx} \left( \sin(6x) - e^{3x} + 4 \right)$ $f(x) = 6\cos(6x) - 3e^{3x}$

So, $f(x) = 6\cos(6x) - 3e^{3x}$.