Logarithmic differentiation means tAke logarithm of both sides to make the function easier to find the derivative.
y = (sinx)^lnx
ln(y) = ln((sinx)^lnx)
power rule logarithm
ln(y) = ln(x) ln(sinx)
Take derivative
y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx
multiply both sides by y
y' = y( ln(sinx)/x + ln(x)cotx )
remember y = (sinx)^lnx
sub this in for y
y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx
To get to 86 by only using 10's and 1's you count by 10, 8 times and count by 1, 6 times.
Its 5 because if u do 3x 5 it equals 15 then subtract 2 it gives u 13
Let d(x) = 2x - 4
Or
y = 2x - 4
We have replace x = y
x = 2y - 4
Now Isolate "y"
x + 4 = 2y
Pass "2" dividing
(x + 4) / 2 = y
y = x/2 + 2
Or
d(x)^-1 = x/2 + 2
