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  • Need solution for RD Sharma Maths Class 12 Chapter 11 Higher Order Derivatives Excercise Multiple Choice Questions Question 8

Need solution for RD Sharma Maths Class 12 Chapter 11 Higher Order Derivatives Excercise Multiple Choice Questions Question 8

Answers (1)

Answer:

                (a)

Hint:

We must know about the derivative of \cos x and \sin x .

Given:

                \begin{aligned} &y=a \sin m x+b \cos m x \\ & \end{aligned}

Explanation:

                  \begin{aligned} &y=a \sin m x+b \cos m x \\ & \end{aligned}

                  \frac{d y}{d x}=a(\cos m x) m+b(-\sin m x) m \\

                  \frac{d y}{d x}=m a \cos m x-m b \sin m x

                 \begin{aligned} &\frac{d^{2} y}{d x^{2}}=m a(-\sin m x) \times m-m b(\cos m x) \times m \\ & \end{aligned}

                 \frac{d^{2} y}{d x^{2}}=-a m^{2}(\sin m x)-m^{2} b(\cos m x)

                 \begin{aligned} &\frac{d^{2} y}{d x^{2}}=-m^{2}[a \sin m x+b \cos m x] \\ & \end{aligned}

                \frac{d^{2} y}{d x^{2}}=-m^{2} y

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