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Find dy/dx.

y=7x^9sin x cos x

Find dy/dx. y=7x^9sin x cos x-example-1

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Answer:

Given: y = 7x^9sin(x)cos(x)

Using the product rule, we differentiate each term separately:

dy/dx = (d/dx)[7x^9sin(x)cos(x)]

= 7[(d/dx)(x^9sin(x)cos(x))] + 7x^9[(d/dx)(sin(x)cos(x))]

Now, let's differentiate each term further using the chain rule:

(dy/dx) = 7[(d/dx)(x^9sin(x)cos(x))] + 7x^9[(d/dx)(sin(x)cos(x))]

= 7[(9x^8sin(x)cos(x)) + (x^9cos^2(x) - x^9sin^2(x))]

= 63x^8sin(x)cos(x) + 7x^9(cos^2(x) - sin^2(x))

Therefore, dy/dx = 63x^8sin(x)cos(x) + 7x^9(cos^2(x) - sin^2(x)).

Explanation:

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