how to find the derivative of y=3tan(piex^2)
using the chain rule?
u = pi x^2
du/dx = 2pi x
v = tan(u)
dv/du = sec^2(u)
y = 3v
dy/dx = 3 dv/dx = 3 sec^2(u) du/dx = 6pi*x*sec^2(pi x^2)
Make that dv/du
To find the derivative of the given function y = 3tan(πex^2) using the chain rule, follow these steps:
1. Identify the inner function, which in this case is πex^2.
2. Compute the derivative of the inner function, which is d/dx (πex^2) = 2πex.
3. Identify the outer function, which is tan( ).
4. Compute the derivative of the outer function, which is d/dx(tan(u)) = sec^2(u) * du/dx, where u is the inner function.
5. Substitute the derivative of the inner function and the inner function itself into the derivative of the outer function:
d/dx(y) = (3sec^2(πex^2)) * (2πex)
So, the derivative of y = 3tan(πex^2) using the chain rule is d/dx(y) = (3sec^2(πex^2)) * (2πex).