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BITSAT 2012

Exam: BITSAT
Year: 2012
Subject: Mathematics
Chapter: Differentiation

BITSAT 2012 · Mathematics · Differentiation

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

If

x=a \sin \theta

and

y=b \cos \theta,

then

\frac{d^{2} y}{d x^{2}}

is

Options

A $\frac{a}{b^{2}} \sec ^{2} \theta$
B $\frac{-b}{a} \sec ^{2} \theta$
C $\frac{-b}{a^{2}} \sec ^{3} \theta$
D $\frac{b}{a^{2}} \sec ^{3} \theta$

Correct answer

B. $\frac{-b}{a} \sec ^{2} \theta$

Step-by-step solution

(b) Given

x=a \sin \theta

and

y=b \cos \theta\Rightarrow \frac{d x}{d \theta}=a \cos \theta

and

\frac{d y}{d \theta}=-b \sin \theta\therefore \quad \frac{d y}{d x}=\frac{d y}{d \theta} \times \frac{d \theta}{d x}=-\frac{b}{a} \tan \theta \Rightarrow \frac{d^{2} y}{d x^{2}}=\frac{-b}{a} \sec ^{2} \theta

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