Math Problem Statement
Solution
The image asks to find the derivative for each of the given functions. Let's go through each part:
a)
- The derivative of is .
- The derivative of is . Thus, .
b)
- The derivative of is .
- The derivative of the constant is 0. Thus, .
c)
- The derivative of is .
- The derivative of is . Thus, .
d)
- The derivative of is .
- The derivative of is . Thus, .
e)
- The derivative of is 0.
- The derivative of is . Thus, .
f)
- The derivative of is .
- The derivative of is . Thus, .
g)
- The derivative of is .
- The derivative of is . Thus, .
h)
- The derivative of is 0.
- The derivative of is .
- The derivative of is . Thus, .
Would you like further details or clarifications on any of these derivatives?
Here are some related questions you might want to explore:
- What is the second derivative of the function in part (a)?
- How do higher powers of affect the shape of the derivative graph?
- Can we apply chain rule in these examples? If so, in what cases?
- How do we differentiate functions with multiple terms like in part (h)?
- What is the physical interpretation of these derivatives in terms of rates of change?
Tip: Remember, constants always differentiate to zero, and powers of follow the power rule for differentiation!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Power Rule
Formulas
d/dx (x^n) = n * x^(n-1)
Theorems
Power Rule for Derivatives
Suitable Grade Level
Grades 11-12
Related Recommendation
Derivative of y = x^4 + 8/x^2 Using Power Rule
Find the Derivatives of Polynomial Functions Using Product and Power Rules
Differentiate Functions with Fractional and Negative Exponents
Step-by-Step Differentiation of Functions Using the Power Rule
Derivative Calculation for Polynomial, Radical, Rational, and Trigonometric Functions