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find dy/dx when y= sin x sin 2x sin 3x sin 4x

find dy/dx when
y= sin x sin 2x sin 3x sin 4x

Grade:11

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
\\ \\ \frac{d}{dx}\left(\sin \left(x\right)\sin \left(2x\right)\sin \left(3x\right)\sin \left(4x\right)\right) \\ f=\sin \left(x\right),\:g=\sin \left(2x\right)\sin \left(3x\right)\sin \left(4x\right) \\ =\frac{d}{dx}\left(\sin \left(x\right)\right)\sin \left(2x\right)\sin \left(3x\right)\sin \left(4x\right)+\frac{d}{dx}\left(\sin \left(2x\right)\sin \left(3x\right)\sin \left(4x\right)\right)\sin \left(x\right)
\\ \frac{d}{dx}\left(\sin \left(x\right)\right) \\ =\cos \left(x\right) \\ \frac{d}{dx}\left(\sin \left(2x\right)\sin \left(3x\right)\sin \left(4x\right)\right) \\ =\cos \left(x\right)\sin \left(2x\right)\sin \left(3x\right)\sin \left(4x\right)+\left(\cos \left(2x\right)2\sin \left(3x\right)\sin \left(4x\right)+\left(\cos \left(3x\right)3\sin \left(4x\right)+\cos \left(4x\right)4\sin \left(3x\right)\right)\sin \left(2x\right)\right)\sin \left(x\right) \\=>2\sin \left(3x\right)\sin \left(4x\right)\cos \left(2x\right)\sin \left(x\right)+\sin \left(2x\right)\left(3\sin \left(4x\right)\cos \left(3x\right)\sin \left(x\right)+\sin \left(3x\right)\left(\sin \left(4x\right)\cos \left(x\right)+4\cos \left(4x\right)\sin \left(x\right)\right)\right) \\
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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