Finding the derivative of compound function: y = e ^ 2x + 2arctan5x

Finding the derivative of compound function: y = e ^ 2x + 2arctan5x

y'=2e^2x+10/(1+25x^2)

It is known that cos x = 1 / 7, cos (X-Y) = 13 / 14 and 0 < y < x < π / 2
Find y

Because 0 < y < x < π / 2, (SiN x) ^ 2 + (COS x) ^ 2 = 1
So SiN x = (4 * 3 ^ (1 / 2)) / 7
cos(x-y)=cos(y-x)=13/14
And - π / 2

The function y = x & # 178; - 4x + 5 is an increasing function in the interval ()

y=x²-4x+4+1
=(x-2)²+1
The opening is upward, and the axis of symmetry x = 2
So it increments to the right of x = 2
So the increasing interval is (2, + ∞)

In which interval is the function f (x) = x & # 178; - 4x + 3 an increasing function and a decreasing function?

f(x)=(x-2)²-1
Axis of symmetry x = 2, opening upward
So (2, + ∞) is an increasing function
(- ∞, 2) is a decreasing function