Math Problem Statement
question number 6
Solution
Let's focus on Question 6 from the provided image, which involves differentiating various functions.
The given functions are:
- (a)
- (b)
- (c)
- (d)
We will differentiate each of these step by step.
(a)
We rewrite the function using a negative exponent:
Using the power rule (), we get:
(b)
We rewrite the square root as a fractional exponent:
Using the power rule:
(c)
We rewrite the function using a negative fractional exponent:
Using the power rule:
(d)
We rewrite the function:
Using the laws of exponents ():
Now differentiate using the power rule:
Final Answers:
- (a)
- (b)
- (c)
- (d)
Would you like a more detailed explanation of any specific part? Let me know!
Here are 5 related questions for practice:
- Differentiate .
- Differentiate .
- Differentiate .
- Differentiate .
- Differentiate .
Tip: Always rewrite roots and fractions using exponents before applying differentiation rules—it simplifies the process.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Power Rule
Exponent Rules
Formulas
Power Rule: d/dx[x^n] = n * x^(n-1)
Laws of Exponents: a^m * a^n = a^(m+n), 1/a^n = a^(-n)
Theorems
-
Suitable Grade Level
Grades 10-12