frac{d}{d x}left(3^{1-2 x}right) = . . . . | vedclass

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Question

(A) To find the derivative of $y = 3^{1-2 x}$,we use the chain rule and the formula $\frac{d}{d x}(a^u) = a^u \cdot \log a \cdot \frac{d u}{d x}$.Here

Vedclass · Accepted Answer

$-2 \cdot 3^{1-2 x} \log 3$

Vedclass · Answer

(A) To find the derivative of $y = 3^{1-2 x}$,we use the chain rule and the formula $\frac{d}{d x}(a^u) = a^u \cdot \log a \cdot \frac{d u}{d x}$.Here,$a = 3$ and $u = 1 - 2x$.First,find the derivative of the exponent: $\frac{d}{d x}(1 - 2x) = -2$.Now,apply the formula:$\frac{d}{d x}(3^{1-2 x}) = 3^{1-2 x} \cdot \log 3 \cdot \frac{d}{d x}(1 - 2x)$$= 3^{1-2 x} \cdot \log 3 \cdot (-2)$$= -2 \cdot 3^{1-2 x} \log 3$.Thus,the correct option is $A$.

$\frac{d}{d x}\left(3^{1-2 x}\right) = $ . . . . . .

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