can you show me how to solve an equation using the chain rule
let y= rqt^3.5 where r, q, t are functions of x
then chain rule is....
y'= dr/dx * qt^3.6 + rt^3.5 *dq/dt + rq dt^3.5/dx
y'= dr/dx * qt^3.6 + rt^3.5 *dq/dt + 3.5rqt^2.5 * dt/dx
that is the chain rule.
so, why toss in the product rule as well?
:-)
Certainly! The chain rule is a method from calculus used to find the derivative of a composite function. To solve an equation using the chain rule, you need to follow these steps:
Step 1: Identify the composite function. This is a function inside another function. For example, in the equation f(g(x)), g(x) is the inner function and f(u) is the outer function.
Step 2: Differentiate the outer function. Take the derivative of the outer function with respect to its variable. Let's denote this derivative as f'(u).
Step 3: Differentiate the inner function. Take the derivative of the inner function with respect to its variable. Denote this derivative as g'(x).
Step 4: Multiply the derivatives. Multiply the derivative of the outer function (f'(u)) with the derivative of the inner function (g'(x)). This gives you f'(u) * g'(x).
Step 5: Simplify. If needed, simplify the expression obtained in step 4.
Step 6: Substitute back. Substitute the original variable of the inner function (g(x)) for u in the expression obtained in step 5. This gives you the final derivative in terms of the original variable x.
By following these steps, you can solve an equation using the chain rule.