If y = x⁶ cos x, find d²y/dx². A) 30x⁴ cos x - 12x⁵ sin x + x⁶ cos x B) 30x⁴ cos x - 6x⁵ sin x - x⁶ cos x C) 30x⁴ cos x - 12x⁵ sin x - x⁶ cos x D) 30x⁴ cos x - 12x⁵ sin x E) 6x⁵ cos x - x⁶ sin x

Question

Quizplus · Accepted Answer

Using the product rule and chain rule, we get: d²y/dx²= [(d/dx)(x²)][⁶ cos x] + [x²][(d/dx)(⁶ cos x)] = [² + x(-12)³][⁶ cos x] + [x²][-⁶ sin x + x(-1)⁵ cos x] = 12x⁵ sin x - 30x⁴ cos x - x⁶ cos x. Therefore, the correct answer is (C).

If Y = X6 Cos X, Find D2y/dx2

If Y = X⁶ Cos X, Find D²y/dx²