Question

G(x)=(cosθsinθ)^4 what's the differential

Answer 1

sin²2θ. (cos θ sin θ). cos 2θ

Explanation:

finding g'(x)

g'(x)

• (x^n)' = nx^(n -1)

= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }

• (cosθ)' = - sinθ
• (sinθ)' = cosθ

= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}

= 4 (cosθsinθ)³{ cos²θ - sin²θ}

• cos²θ - sin²θ = cos 2θ
• 2sinθ cosθ = sin 2θ

= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}

= sin²2θ. (cos θ sin θ). cos 2θ