Math Problem Statement
احسب مشتقة الدالة g
احسب مشتقة الدالة g
Solution
The given function is:
To find the derivative , we will use the following rules of differentiation:
- The derivative of is given by .
- The derivative of is .
- The power rule for derivatives, .
Now, let's compute the derivative of each term.
Step 1: Derivative of
We can rewrite as . By applying the chain rule:
Step 2: Derivative of
This is . Using the rule for , we get:
Final derivative
Putting it all together:
This is the derivative of the given function.
Would you like any further explanation or details?
Related Questions:
- How can the chain rule be applied to other functions?
- What is the second derivative of this function ?
- How would you compute the derivative of a product of two functions?
- How do you differentiate a function with multiple variables?
- Can you explain the process of implicit differentiation?
Tip:
Always simplify functions as much as possible before differentiating to avoid unnecessary complexity.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Chain Rule
Power Rule
Formulas
Derivative of sqrt(x): d/dx(sqrt(x)) = 1/(2sqrt(x))
Derivative of 1/x: d/dx(1/x) = -1/x^2
Power Rule: d/dx[x^n] = n*x^(n-1)
Theorems
Chain Rule
Power Rule
Suitable Grade Level
University Level