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:
B
To find the first derivative of the function y = e^{-x} with respect to x, we will apply the rules of differentiation.
Step 1: Identify the function:
Here, y = e^{-x}.
Step 2: Differentiate the function:
The derivative of e^{u} with respect to x is e^{u} \cdot \frac{du}{dx}. Here, u = -x.
Therefore, \frac{du}{dx} = -1.
Using the chain rule:
\frac{dy}{dx} = e^{-x} \cdot (-1) = -e^{-x}.
Thus, the first derivative of y with respect to x is -e^{-x}.
Therefore, the correct answer option is B: y' = -e^{-x}.
Step 1: Identify the function:
Here, y = e^{-x}.
Step 2: Differentiate the function:
The derivative of e^{u} with respect to x is e^{u} \cdot \frac{du}{dx}. Here, u = -x.
Therefore, \frac{du}{dx} = -1.
Using the chain rule:
\frac{dy}{dx} = e^{-x} \cdot (-1) = -e^{-x}.
Thus, the first derivative of y with respect to x is -e^{-x}.
Therefore, the correct answer option is B: y' = -e^{-x}.
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