Question

Find the Derivative (dy/dx) of the following problem:

Answer 1

\[y=\cot ^{2} 5x \sin5x \]

Answer 2

\[\frac{ dy }{ dx }=2\cot 5x \left( -\csc ^25x \right)*5\sin 5x+2\cot ^25x*\cos 5x*5\]
\[=10\cot 5x \sin 5x \left( -\csc ^25x+\cot 5x \right)\]
?

Answer 3

What happened to the cot5x and the cot^2 5x?
@surjithayer

Answer 4

Did you get first step?

Answer 5

\[\frac{ dy }{ dx }=2\cot 5x \left( -cosec ^25x \right) \cdot5\sin 5x+2\cot ^25x \cdot \cos 5x \cdot 5\]

Answer 6

I understand that step, i am just confused of how you simplify it...

Answer 7

I would simplify first, then find the derivative
cot = cos/sin

and cot^2 5x * sin 5x = cos^2 5x / sin^2 5x * sin 5x =cos^2 5x / sin 5x
= (1- sin^2 5x) / sin 5x = 1/ sin 5x - sin 5x
now take the derivative.

Answer 8

thanks