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

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

Answers (1)

Answer:

        2e^{x}cos(x+\frac{\pi }{2})

Hint:

You must know about derivative of  ex cos x

Given:

If y = ex cos x, prove that

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

Solution:

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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