What is the first differential of #Y(x) = sinx*lnx# ?

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Answer 1 · 2017-12-09T03:15:57

#(dY)/dx = sinx/x + lnxcosx#

#Y(x) = sinx*lnx#

We will use the product rule and standard differentials.

The product rule states that for two functions of #x; f(x) and g(x)#
Then:

#d/dx (f(x) * g(x)) = f(x) * d/dx g(x) + g(x) * d/dx f(x)#

In this example #f(x) = sinx and g(x) = lnx#

#Y(x) = f(x) * g(x)#

#:. (dY)/dx = sinx * d/dx lnx + lnx * d/dx sinx#

Apply standard differentials.

#(dY)/dx = sinx *1/x + lnx *cosx#

#= sinx/x + lnxcosx#