Find dydx if x-acos- - -sin- and y-asin- - -cos-

Given x=a(cos θ+ θsinθ) and #160; y=a(sin θ θcosθ) We need to find dydx dyd θ = a(cos θ cos θ +θ sin θ)=a( θ sin θ) Similarly , we get ...

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Derivative of Standard Functions

Find dydx i...

Question

Find $\frac{d y}{d x}$ if $x = a (cos θ + θ sin θ)$ . and $y = a (sin θ - θ cos θ)$ .

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Solution

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\frac{d y}{d x}

x = a (\cos θ + θ \sin θ) and y = a (\sin θ - θ \cos θ)

x = a (cos θ + θ sin θ), y = a (sin θ - θ cos θ),

\frac{d^{2} x}{d θ^{2}} = a (cos θ - θ sin θ), \frac{d^{2} y}{d θ^{2}} = a (sin θ + θ cos θ)

\frac{d^{2} x}{d θ^{2}} = a (\cos θ - θ \sin θ), \frac{d^{2} y}{d θ^{2}} = a (\sin θ + θ \cos θ) and \frac{d^{2} y}{d x^{2}} = \frac{\sec^{3} θ}{a θ} .

x = a (cos θ + θ sin θ)

y = a (sin θ - θ cos θ)

\frac{d y}{d x}

x

y

\frac{d y}{d x}

x = a (cos θ + θ sin θ), y = a (sin θ - θ cos θ)

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