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  • Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 11

Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 11

Answers (1)

Answer:

        \frac{-b}{a^{2}y^{3}}

Hint:

You must know about derivative of second order

Given:

\begin{aligned} &{\text { If } x}=a \cos \theta, y=b \sin \theta \\ &\text { Show that } \frac{d^{2} y}{d x^{2}}=\frac{-b}{a^{2} y^{3}} \end{aligned}

Solution:

\begin{aligned} &{\text {Let}\: \: x}=a \cos \theta, y=b \sin \theta \\ \end{aligned}

        \begin{aligned} &\frac{d y}{d x}=\frac{\frac{d y}{d \theta}}{\frac{d x}{d \theta}} \\ &\frac{d^{2} y}{d x^{2}}=\frac{\frac{d}{d \theta}\left(\frac{d y}{d x}\right)}{\frac{d x}{d \theta}} \\ &x=a \cos \theta, y=b \sin \theta \\ &\frac{d x}{d \theta}=-a \sin \theta \frac{d y}{d \theta}=b \cos \theta \\ &\frac{d y}{d x}=\frac{-b}{a} \cot \theta \end{aligned}

        \begin{aligned} &\frac{\frac{\mathrm{d} }{\mathrm{d} \theta }(\frac{dy}{dx})}{\frac{dx} {d\theta }}=\frac{\frac{b}{a} \cos e c^{2} \theta}{-a \sin \theta} \quad\left(\frac{d}{d \theta} \cot \theta=\cos e c^{2} \theta\right) \\ &\frac{-b \times b^{3}}{a^{2} \sin ^{3} \theta \times b^{3}} \\ &\frac{d^{2} y}{d x^{2}}=\frac{-b}{a^{2} y^{3}} \end{aligned}

Hence proved

Posted by

Gurleen Kaur

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