Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Find the value of 
.
Text Solution
Verified by ExpertsThe correct answer is:
A
To find the derivative of the function \( (Ax + B)^n \), we can apply the chain rule.
Step 1: Identify the outer function and inner function. Let \( u = Ax + B \). Hence, we have:
\( (Ax + B)^n = u^n \).
Step 2: Differentiate using the chain rule: \( \frac{d}{dx}(u^n) = n u^{n-1} \cdot \frac{du}{dx} \).
Step 3: Now, find \( \frac{du}{dx} \): \( \frac{du}{dx} = A \).
Step 4: Substitute back into the derivative: \( \frac{d}{dx}(Ax + B)^n = n(Ax + B)^{n-1} \cdot A \).
Step 5: Therefore, the final answer is:
\( \frac{d}{dx}(Ax + B)^n = nA(Ax + B)^{n-1}.
Therefore, A.
Step 1: Identify the outer function and inner function. Let \( u = Ax + B \). Hence, we have:
\( (Ax + B)^n = u^n \).
Step 2: Differentiate using the chain rule: \( \frac{d}{dx}(u^n) = n u^{n-1} \cdot \frac{du}{dx} \).
Step 3: Now, find \( \frac{du}{dx} \): \( \frac{du}{dx} = A \).
Step 4: Substitute back into the derivative: \( \frac{d}{dx}(Ax + B)^n = n(Ax + B)^{n-1} \cdot A \).
Step 5: Therefore, the final answer is:
\( \frac{d}{dx}(Ax + B)^n = nA(Ax + B)^{n-1}.
Therefore, A.
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