If y = x^2 + cos(2x) + e^{ax},then find frac{ | vedclass

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(A) Given the function $y = x^2 + \cos(2x) + e^{ax}$.To find the derivative $\frac{dy}{dx}$,we differentiate each term with respect to $x$ using the s

Vedclass · Accepted Answer

$2x - 2\sin(2x) + ae^{ax}$

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(A) Given the function $y = x^2 + \cos(2x) + e^{ax}$.To find the derivative $\frac{dy}{dx}$,we differentiate each term with respect to $x$ using the sum rule:$\frac{dy}{dx} = \frac{d}{dx}(x^2) + \frac{d}{dx}(\cos(2x)) + \frac{d}{dx}(e^{ax})$.Using the power rule,$\frac{d}{dx}(x^2) = 2x$.Using the chain rule for the trigonometric function,$\frac{d}{dx}(\cos(2x)) = -\sin(2x) \cdot \frac{d}{dx}(2x) = -\sin(2x) \cdot 2 = -2\sin(2x)$.Using the chain rule for the exponential function,$\frac{d}{dx}(e^{ax}) = e^{ax} \cdot \frac{d}{dx}(ax) = e^{ax} \cdot a = ae^{ax}$.Combining these results,we get $\frac{dy}{dx} = 2x - 2\sin(2x) + ae^{ax}$.Thus,the correct option is $A$.

If $y = x^2 + \cos(2x) + e^{ax}$,then find $\frac{dy}{dx}$.

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