Question

d/dx(xpower cos inverse x) differentiate with respect to x by taking log​

Answer 1

Answer:

Let

y = x^cos ^-1 X. .........(1)

taking log on both sides

log y = log X ^ cos ^-1 x

we know that. ( log m^n = n log m )

applying this property

log y = cos ^-1 X log X

differentiating on both sides with respect to "X"

using chain multiplication rule of differentiation.

so,

1/y dy/dx = cos ^-1 X d/dx log x +

log X f/dx cos ^-1 X

1/y dy /dx = cos ^-1x.1/X

+ log X .(-1/√1-x^2)

dy =y( cos^-1x. _ log X. )

---- --------------- --------------

dx. X √ 1-x^2

put the value of y from (1)

dy.= X ^cos ^-1x ( cos^-1x. _ log X)

-----. -------------. --------

dx X √1-x^2

hey mate refer to the attachment,

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