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  • Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 1 subquestion (viii) maths

Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 1 subquestion (viii) maths

Answers (1)

Answer:

        -xcos\: x-2sin\: x

Hint:

You must know about derivative of x cos x

Given:

        x cos x

Solution:

Let\: \: xcos\: x

Use multiplicative rule

As  UV=UV1+U1V

Where  U=x & V=cos x

        \begin{aligned} &\frac{d y}{d x}=x \frac{d}{d x} \cos x+\frac{d}{d x} x \cos x \quad\left(\frac{d}{d x} x=1, \frac{d}{d x} \cos x=-\sin x\right) \\ &\frac{d y}{d x}=-x \sin x+\cos x \end{aligned}

Use multiplicative rule

As  UV=UV1+U1V

Where  U=x & V=sin x

        \begin{aligned} &\frac{d^{2} y}{d x^{2}}=-\left(x \frac{d}{d x} \sin x+\frac{d}{d x} x \cdot \sin x\right)+\frac{d \cos x}{d x} \\ &\frac{d^{2} y}{d x^{2}}=-(x \cos x+\sin x)-\sin x \quad\left(\frac{d}{d x} \cos x=-\sin x\right) \\ &\frac{d^{2} y}{d x^{2}}=-x \cos x-\sin x-\sin x \\ &\frac{d^{2} y}{d x^{2}}=-x \cos x-2 \sin x \end{aligned}

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Gurleen Kaur

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