derivative help!?

Question

how do you find the derivative of:

1. y=(sin x) ^ x

2. y= x ^ (1-e)

3. y= x ^ - sq root(2)

Answer 1

1. y=(sin x) ^ x
ln(y)= xln(sinx)
y'/y = ln(sin x) +x(1/sinx)cosx
y' = y[ln(sinx)+ x cotx] = (sinx)^x[ln(sinx)+ x cotx]

2. y= x ^ (1-e)
y= x/x^e
y' =[x^e -x*e*x^(e-1)]/x^(2e)
y' = (x^e-ex^e)/x^(2e)
y' = (1-e)/x^e

3. y= x ^ - sq root(2)
y' = x^(-1-sqrt(2))(-sqrt(2))

Answer 2

pass away 6 out first. pondering x^4/a million-x write x^4= x^3*x, so as that we are in a position to write the expression as x^3(x+a million-a million)/a million-x. separate it out like x^3(x-a million)/a million-x+x^3/a million-x, this leads to (-x^3)+(x^3/a million-x) because of the fact the utmost capacity of this expression is 3 and you should locate the fourth derivative so all would be 0.

Answer 3

log y = x log sin x
y ' / y = x cos x + log sin x
y ' = y (x cos x + log sin x)
y ' = (sin x)^x (x cos x + log sin x)

log y = (1-e) log x
y ' / y = (1-e) (1/x)
y ' = y (1-e) (1/x)
y ' = x^(1-e) (1-e) (1/x)

similar process is also done to the rest

Answer 4

1. (x cotangent (x) + ln (sine (x))) sine (x)^x

I can't do the other two. Sorry. What do you mean with 'e' and '- sqrt(2)'???