HSC Arts 12th Board ExamMaharashtra State Board
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# Find the value of dy/dx at θ=pi/4 if x=ae^θ (sinθ-cosθ) and y=ae^θ(sinθ+cosθ) - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptDerivatives of Functions in Parametric Forms

#### Question

Find the value of dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)

#### Solution

y=ae^theta(sintheta+cos theta)

x=ae^theta (sintheta-costheta)

Differentiating y with respect to θ on both the sides, we get:

dy/(d theta)=ae^theta(costheta-sintheta)+ae^theta(sintheta+costheta)dy/(d theta)

=2ae^theta cos theta

Differentiating x with respect to θ on both the sides, we get:

dx/(d theta)=ae^theta(costheta+sintheta)+ae^theta(sintheta-costheta)dx/(d theta)

=2ae^theta sin theta

Now

dy/dx=(dy/(d theta))/(dx/(d theta))=(2ae^theta cos theta)/(2ae^theta sin theta)=cot theta

(dy/dx)_(theta=pi/4)=cot(pi/4)=1

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Solution Find the value of dy/dx at θ=pi/4 if x=ae^θ (sinθ-cosθ) and y=ae^θ(sinθ+cosθ) Concept: Derivatives of Functions in Parametric Forms.
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