Differentiating sine

If y=a\sin bx, then \frac{dy}{dx}=ab\cos bx

Find \frac{dy}{dx} of y=2\sin x

• \frac{dy}{dx}=2\cos x

Find \frac{dy}{dx} of y=\sin3x

• \frac{dy}{dx}=3\cos3x

Find \frac{dy}{dx} of y=2\sin5x

• \frac{dy}{dx}=2(5\cos5x)
• \frac{dy}{dx}=10\cos5x

Find \frac{dy}{dx} of y=-3\sin(-2x)

• \frac{dy}{dx}=-3(-2\cos(-2x))
• \frac{dy}{dx}=6\cos(-2x)

Find \frac{dy}{dx} of y=10\sin\frac x2

• \frac{dy}{dx}=10(\frac x2\cos(\frac x2))
• \frac{dy}{dx}=5x\cos\frac x2

Find \frac{dy}{dx} of y=\tan4x\cdot\cos4x

• y=\frac{\sin4x}{\cos4x}\cdot\cos4x
• y=\sin4x
• \frac{dy}{dx}=4\cos4x

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