If x = a sin θ and y = b cos θ , then d x 2 d 2 y is

(b) Given x = a sin θ and y = b cos θ ⇒ d θ d x = a cos θ and d θ d y = − b sin θ ∴ d x d y = d θ d y × d x d θ = − a b tan θ ⇒ d x 2 d 2 y = a − b sec 2 θ

Mathematics - Differentiation Question with Solution | TestHub

MathematicsDifferentiationHigher Order DifferentiationEasy2 minPYQ_2012

MathematicsEasysingle choice

If $x = a sin θ$ and $y = b cos θ,$ then $\frac{d ^{2} y}{d x ^{2}}$ is

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Answer:

Solution:

(b) Given $x = a sin θ$ and $y = b cos θ$ $\Rightarrow \frac{d x}{d θ} = a cos θ$ and $\frac{d y}{d θ} = - b sin θ$ $∴ \frac{d y}{d x} = \frac{d y}{d θ} \times \frac{d θ}{d x} = - \frac{b}{a} tan θ \Rightarrow \frac{d ^{2} y}{d x ^{2}} = \frac{- b}{a} sec^{2} θ$

Stream:BITSATSubject:MathematicsTopic:DifferentiationSubtopic:Higher Order Differentiation

⏱ 2mℹ️ Source: PYQ_2012

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