Question

F(x)=2x•e^x-tgx Найти f’(0)

Answer 1

F(x)=2x•e^x-tgx
F(x)=0*1-0=0 

Answer 2

f'(x) = 2*e^x+2x*e^x-1/cos^2x

Answer 3

To find the derivative of the function $F(x) = 2x \cdot e^x - \tan(x)$ and then evaluate it at $x = 0$, we'll follow these steps:

Step 1: Find the derivative of $F(x)$ with respect to $x$. Step 2: Evaluate the derivative at $x = 0$ to find $F'(0)$.

Let's start with Step 1:

$F(x) = 2x \cdot e^x - \tan(x)$

To find the derivative, we'll use the sum/difference rule and the product rule:

$F'(x) = (2x)' \cdot e^x + 2x \cdot (e^x)' - (\tan(x))'$

Now, we need to find the derivatives of the individual terms:

$(2x)' = 2$ $(e^x)' = e^x$ $(\tan(x))' = \sec^2(x)$

Now, let's plug these back into the equation for $F'(x)$:

$F'(x) = 2 \cdot e^x + 2x \cdot e^x - \sec^2(x)$

Now, for Step 2, we need to find $F'(0)$:

$F'(0) = 2 \cdot e^0 + 2 \cdot 0 \cdot e^0 - \sec^2(0)$

Since $e^0 = 1$ and $\sec(0) = 1$, we get:

$F'(0) = 2 \cdot 1 + 0 - 1$

$F'(0) = 1$

Therefore, the value of the derivative $f'(0)$ of the given function at $x = 0$ is $1$.