The above is close. The -0.5l^(-.05) term should be -0.5l^(-0.5). I don't know if that was a transcription error. Also, the exponential term would be clearer as (1/2)e(x/10).939 said:Homework Statement
If possible, please check my work for any large errors.
y = 10kl - √k - √l
k = (t/5) + 5
l = 5e^t/10
Evaluate at t = 0 using chain rule.
Homework Equations
y = 10kl - √k - √l
k = (t/5) + 5
l = 5e^t/10
The Attempt at a Solution
= ∂y/∂k * dk/dt + ∂y/∂l * dl/dt
= (10l - 0.5K^-0.5)(1/5) + (10k - 0.5l^-.05)((e^(x/10))/2)
k(0) and l(0) are fine, but I didn't check your other numbers.939 said:k(0) = 5
l(0) = 5
y(0) = ~9.95 + ~41.03 = ~51
The chain rule is a calculus rule that allows us to find the derivative of a composite function. In the context of partial derivatives, it helps us find the rate of change of a multivariable function with respect to one of its variables while holding the other variables constant.
To check if you have correctly applied the chain rule in a partial derivative, you should make sure that the inner and outer functions are properly identified and that the derivative of the inner function is multiplied by the derivative of the outer function.
Some common mistakes when using the chain rule in partial derivatives include forgetting to identify the inner and outer functions, misapplying the power rule, and not properly simplifying the expression after applying the chain rule.
Checking our work when using the chain rule in partial derivatives is important to ensure that we have correctly applied the rule and have not made any algebraic or computational errors. This helps us avoid incorrect solutions and better understand the concepts involved.
Some tips for effectively using the chain rule in partial derivatives include carefully identifying the inner and outer functions, practicing with different types of functions, and simplifying the expression as much as possible before taking the derivative.