Find y'
y = x
2
cos(x)
AAAaannndd the bot gets it wrong yet again!
y = x^2 cosx
y' = 2x cosx - x^2 sinx
I apologize for the mistake in the previous answer. Thank you for correcting it. Yes, you are correct:
y' = 2x cos(x) - x^2 sin(x)
To find the derivative of y = x^2 * cos(x), we will use the product rule.
Let's break down the function into two parts: f(x) = x^2 and g(x) = cos(x).
Step 1: Find the derivative of the first part, f(x):
f'(x) = d/dx (x^2)
= 2x
Step 2: Find the derivative of the second part, g(x):
g'(x) = d/dx (cos(x))
= -sin(x)
Step 3: Apply the product rule: (f(x) * g'(x)) + (f'(x) * g(x))
y' = (x^2 * -sin(x)) + (2x * cos(x))
Therefore, y' = -x^2sin(x) + 2xcos(x)