Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Find first derivative of 
w.r.t. 
.
(i) 
(ii) 
(iii) 
Text Solution
Verified by ExpertsThe correct answer is:
C
To find the first derivative of the function with respect to x, we need to apply the appropriate differentiation rules.
Step 1: Identify the given function. For option (iii), the function is y = 4e^{x^2 - 2x}.
Step 2: To differentiate this function, we use the chain rule. The derivative of e^u is e^u * du/dx, where u = x^2 - 2x.
Step 3: Compute du/dx:
u = x^2 - 2x \implies du/dx = 2x - 2.
Step 4: Now apply the chain rule:
dy/dx = 4 \cdot e^{x^2 - 2x} \cdot (2x - 2).
Result: Therefore, the first derivative is given by dy/dx = 4e^{x^2 - 2x}(2x - 2).
Hence, option (iii) is correct.
Step 1: Identify the given function. For option (iii), the function is y = 4e^{x^2 - 2x}.
Step 2: To differentiate this function, we use the chain rule. The derivative of e^u is e^u * du/dx, where u = x^2 - 2x.
Step 3: Compute du/dx:
u = x^2 - 2x \implies du/dx = 2x - 2.
Step 4: Now apply the chain rule:
dy/dx = 4 \cdot e^{x^2 - 2x} \cdot (2x - 2).
Result: Therefore, the first derivative is given by dy/dx = 4e^{x^2 - 2x}(2x - 2).
Hence, option (iii) is correct.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems