how do not understand how to find a deriviative of this function?Do i use chain rule and product rule?
r= the square root of (theta*sin*theta)
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ok, if f(u) exists, and u=G(x)
then
y= f(u)
dy/dx= d(f(u)/du * du/dx
but u=G(x)
so du/dx= G'
Now in practice.
r= sqrt(Theta*sinTheta)
dr/dtheta= 1/2 (1/sqrt(Theta*sinTheta))* d(theta*sinTheta)/dtheta
and d(theta*sinTheta)/dtheta= sinTheta+ theta*cosTheta.
To find the derivative of the function r = sqrt(theta*sin(theta)), we can indeed use the chain rule and the product rule.
Let's break down the steps:
Step 1: Apply the product rule.
The product rule states that if we have a function h(x) = f(x) * g(x), then its derivative can be found as h'(x) = f'(x) * g(x) + f(x) * g'(x).
In our case, we can rewrite the function as r = (theta * sin(theta))^0.5. So, let f(theta) = theta and g(theta) = sin(theta).
Step 2: Find the derivative of f(theta) using the chain rule.
The chain rule states that if we have a composite function h(x) = f(g(x)), then its derivative is given by h'(x) = f'(g(x)) * g'(x).
In our case, f(theta) = theta, so f'(theta) = 1. Notice that g(theta) = sin(theta) within f(theta). To find g'(theta), we can use the derivative of sin(theta), which is cos(theta). So, we have f'(g(theta)) = 1 and g'(theta) = cos(theta).
Step 3: Apply the product rule to find the derivative of the function.
Using the product rule, we have r' = f'(theta) * g(theta) + f(theta) * g'(theta).
Substituting the derivatives we found, r' = 1 * sin(theta) + theta * cos(theta).
Therefore, the derivative of r = sqrt(theta*sin(theta)) with respect to theta is r' = sin(theta) + theta * cos(theta).
Remember, when using the chain rule and product rule, it is important to understand the individual functions involved and their derivatives.