Hello,
Could somebody kindly check my answer for the following question?
Find the derivative of the following function:
h(x)=3e^(sin(x+2))
h'(x)=3'(e^(sin(x+2))+3(e^(sin(x+2))'
h'(x)=0(e^(sin(x+2))+3(e^(sin(x+2))(cos(1))
h'(x)=3cos1(e^(sin(x+2))
I would greatly appreciate your help.
Constantine
you can always check your answers at wolframalpha.com
As you can see, you're way off.
If h = 3e^u where u is a function of x, then
h' = 3e^u du/dx
= 3e^(sin(x+2)) * cos(x+2)
http://www.wolframalpha.com/input/?i=derivative+3e^%28sin%28x%2B2%29%29
Thank you Steve.
Hello Constantine,
To find the derivative of the given function, h(x) = 3e^(sin(x+2)), we can use the chain rule. The steps you've shown in your answer are mostly correct, but there are a few mistakes.
Let's go through the process step by step:
1. Start with the function h(x) = 3e^(sin(x+2)).
2. Apply the chain rule, which states that if we have a function g(f(x)), the derivative can be found by multiplying the derivative of the outer function g'(f(x)) with the derivative of the inner function f'(x).
3. Identify the outer function g(x) = 3e^x, and the inner function f(x) = sin(x+2).
4. Take the derivative of the outer function g'(x), which is simply a constant, so g'(x) = 3.
5. Take the derivative of the inner function f'(x) using the chain rule. The derivative of sin(x) is simply cos(x), and since we have sin(x+2), we need to account for the chain rule by multiplying with the derivative of the inside function, which is (x+2)' = 1. So, f'(x) = cos(x+2).
6. Now, we multiply g'(f(x)) with f'(x) to get the derivative of h(x): h'(x) = g'(f(x)) * f'(x) = 3 * cos(x+2).
So, the correct derivative of h(x) = 3e^(sin(x+2)) is h'(x) = 3cos(x+2).
Therefore, your final step should be: h'(x) = 3cos(x+2).
I hope this explanation helps. Let me know if you have any further questions.