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Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 10

Answers (1)


        2e^{x}cos(x+\frac{\pi }{2})


You must know about derivative of  ex cos x


If y = ex cos x, prove that

        \frac{d^{2}y}{dx^{2}}=2e^{x}cos(x+\frac{\pi }{2})


Let y = ex cos x

Use multiplicative rule

        \begin{aligned} &\text { As } U V=U V^{1}+U^{1} V \\ &\text { Where } U=e^{x}\: \&\: V=\cos x \\ &\frac{d y}{d x}=e^{x}(-\sin x)+e^{x} \cos x \quad \quad\left(\frac{d}{d x} \cos x=\sin x\right) \end{aligned}

Again Use multiplicative rule

Differentiating again

        \begin{aligned} &\frac{d^{2} y}{d x^{2}}=-\left[e^{x} \cos x+\sin x e^{x}\right]+\left[-e^{x} \sin x+e^{x} \cos x\right] \\ &\frac{d^{2} y}{d x^{2}}=-2 \sin x e^{x} \\ &\frac{d^{2} y}{d x^{2}}=2 e^{x} \cos \left(x+\frac{\pi}{2}\right) \end{aligned}

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Gurleen Kaur

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