urgent:trigonometric equation help and a few other questions

[lhl_anecar]

once again, thanks for all u guys who had helped me out, couldnt have done it without ur help..
i just need to clarify this..

y=x^5e^x + 3xlnx

how do i differentiate lnx? and how do i do the whole thing with product rule??

[ashish]

once again, thanks for all u guys who had helped me out, couldnt have done it without ur help..
i just need to clarify this..

y=x^5e^x + 3xlnx

how do i differentiate lnx? and how do i do the whole thing with product rule??

^d(lnx)/_dx is 1/x *1
                                             =1/x

the one is the differential of x

let take another example
^d(ln5x)/<sub>dx]  = (1/5x)*5
                                       = 1/x

in general ^d(lnf(x)) /dx  is (1/f(x)) * ^d(fx)/dx


PRODUCT rule is use when you have two products ..

for example

Xlnx is a product

take one term as u and the other as v
u=X
^du/dx = 1

v= lnx
^dv/dx= 1/x


then use this formula
^dy/dx = U^dv/dx + V^du/dx
                                       = x(1/x) + (lnx)*1
                                       =1+lnx

y=x^5ex + 3xlnx


y=x^5ex
note: there is no product here so no product rule

^dy/^dx= 5e^xX^5ex-1--------------------1

3xlnx is a product
take u as 3x
^du/dx = 3

take v as lnx
^dv/dx=(1/x)*1
                                      = 1/x

now us the formula
^dy/dx = U^dv/dx + V^du/dx
                                        = (3x)*(1/x) +(lnx)*3
                                        = 3+3lnx---------------2
now as these two


5e^xX^5ex-1+ 3+3lnx</sub>

[Deadly_king]

Hey buddy........I think the question is as follows:

y = x⁵e^x + 3xln x

Differentiation of ln x is always equal to 1/x.

You need to do this question step by step. Firstly, using the product rule differentiate x⁵e^x.

Then, using the product rule again, differentiate 3xln x.

Add the two results you obtain

By the way nice try ashish
+rep

[ashish]

Hey buddy........I think the question is as follows:

y = x⁵e^x + 3xln x

Differentiation of ln x is always equal to 1/x.

You need to do this question step by step. Firstly, using the product rule differentiate x⁵e^x.

Then, using the product rule again, differentiate 3xln x.

Add the two results you obtain

By the way nice try ashish
+rep

ok ok then the whole question changes
and thanks   

[Deadly_king]

ok ok then the whole question changes
and thanks   

Yupz

Anytime