數學differentiate一問

y=x^9sinx
dy/dx
=d/dx(x^9sinx)
=(x^9)d/dx(sinx)+(sinx)d/dx(x^9)
=(x^9)cosx+sinx(9x^8)
=(x^8)(xcosx+9sinx)

兩個答案同一個人只不過係多左幾句野,,,咁無咩理由投票俾你的

用Product Rule，即係
dy/dx=x^9 7x^6+9x^8 x^7

不過對於呢條問題，冇理由用Product Rule，
因為可以一次過整做 y=x^16用Power Rule咪得囉。

兩個答案一樣，遲左 22 分鐘先至回答，有乜理由叫人投票俾你？

differentiate y=x^9sinx

要differentiate "y=x^9sinx" 呢個 function 要採用 product rule

Sol: .....y=x^9sinx

.....dy/dx=(x^9) d(sinx)dx + (sinx) d(x^9)dx

.....dy/dx=(x^9) (cosx) + (sinx)(9x^(9-1))

.....dy/dx= (x^9)(cosx) + (9x^8)(sinx)...............The Answer

Therefore, differentiate "y=x^9sinx", which results in "dy/dx= (x^9)(cosx) + (9x^8)(sinx)".

Explanation: When you differentiate the function in product terms, you need to apply the "Product Rule of the Differentiation".