4.
ex sin x log x
differentiate using product rule
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y=e^x sinx logx
dy/dx=sinx logx de^x/dx + e^x logx dsinx/dx + e^x sinx dlogx/dx
=sinx logx e^x + e^x logx cosx + e^x sinx 1/x
(as differentiation of sinx is cosx
differentiation of logx is 1/x
and differentiation of e^x is e^x)
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The derivative of the function is .
Explanation:
Given:
The function .
To Find:
The derivative of the function .
Formula used:
A function y = u v, where u and v are the functions of x. Then, by the use of the product rule, we can easily find out the derivative of y with respect to x, and can be written as:
Solution:
As given,the function .
Thus,the derivative of the function is .
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