Find the derivative: frac{d}{dx}(e^{x + 3log | vedclass

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Question

(A) Given the function $y = e^{x + 3\log x}$.Using the properties of exponents and logarithms,we can simplify the expression:$y = e^x \cdot e^{3\log x

Vedclass · Accepted Answer

$e^x \cdot x^2(x + 3)$

Vedclass · Answer

(A) Given the function $y = e^{x + 3\log x}$.Using the properties of exponents and logarithms,we can simplify the expression:$y = e^x \cdot e^{3\log x} = e^x \cdot e^{\log(x^3)} = e^x \cdot x^3$.Now,differentiate $y$ with respect to $x$ using the product rule $\frac{d}{dx}(uv) = u\frac{dv}{dx} + v\frac{du}{dx}$:$\frac{dy}{dx} = \frac{d}{dx}(e^x \cdot x^3) = e^x \cdot \frac{d}{dx}(x^3) + x^3 \cdot \frac{d}{dx}(e^x)$.$\frac{dy}{dx} = e^x \cdot (3x^2) + x^3 \cdot (e^x)$.Factor out $e^x \cdot x^2$:$\frac{dy}{dx} = e^x \cdot x^2(3 + x)$.Thus,the correct option is $A$.

Find the derivative: $\frac{d}{dx}(e^{x + 3\log x}) = $

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