Question

F(x)=(5tg(x/5)+tg(π/8))'

Answer 1

$f'(x)= \frac{1}{cos^2 \frac{x}{5} }$

Answer 2

To find the derivative of the given function F(x) = (5tan(x/5) + tan(π/8)) with respect to x, we'll apply the rules of differentiation.

Let's break down the function into its two components:

1. 5tan(x/5)
2. tan(π/8)

The derivative of tan(x) is sec^2(x), so the derivative of tan(x/5) with respect to x is:

d/dx [tan(x/5)] = sec^2(x/5) * (1/5)

The derivative of tan(π/8) with respect to x is 0 because it's a constant value.

Now, let's find the derivative of the entire function F(x):

F(x) = (5tan(x/5) + tan(π/8))

F'(x) = d/dx [5tan(x/5)] + d/dx [tan(π/8)] F'(x) = 5 * (sec^2(x/5) * (1/5)) + 0 F'(x) = sec^2(x/5)

So, the derivative of the function F(x) is F'(x) = sec^2(x/5).