Question

If y = cos⁴ 0, x = sin⁴ 0, then find dy/dx​

Answer 1

Step-by-step explanation:

We have,

$\rm{y =cos^{4} ( \theta) \: \: \: \: , \: \: \: \: x = sin^{4} ( \theta) }$

Differentiating both sides w.r.t θ,

$\rm{ \dfrac{dy }{d \theta}= - 4 \: cos^{3} ( \theta) \: sin( \theta) \: \: \: \: , \: \: \: \: \dfrac{dx}{d \theta} = 4 \: sin^{3} ( \theta) \: cos( \theta) }$

On dividing, we get,

$\rm{ \dfrac{dy }{dx}= \dfrac{- 4 \: cos^{3} ( \theta) \: sin( \theta) }{ 4 \: sin^{3} ( \theta) \: cos( \theta)} }$

$\rm{ \implies \dfrac{dy }{dx}= - \dfrac{cos^{2} ( \theta) }{ sin^{2} ( \theta) } }$

$\rm{ \implies \dfrac{dy }{dx}= -cot^{2} ( \theta) }$