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need help with derivatives please :)?
1a) Find the derivatives of the following functions:
1) f(x) = (ln x) /x
(2) f(x) = 2xe^3x + 2^x.
b) Use logarithmic differentiation to find the derivatives of the functions:
(i) y = (x + 1)^20(x + 2)^30
(ii) y = (ln x)^x.
1 Answer
- ?Lv 67 years ago
1) f(x) = (ln x) /x
x(1/x)-1(ln(x))/x^2=
(1-ln(x))/x^2
(2) f(x) = 2xe^3x + 2^x
2e^3x+6xe^3x+2^xln2
b) Use logarithmic differentiation to find the derivatives of the functions:
(i) y = (x + 1)^20(x + 2)^30
lny=20ln(x+1)+30ln(x+2)
y'/y=20/x+1+30/x+2
y'= (x + 1)^20(x + 2)^30*[20/x+1+30/x+2]
(ii) y = (ln x)^x.
lny=xln(ln(x))
y'/y=ln(lnx)+x[1/xln(x)]=
ln(ln(x))+1/ln(x)
y'= (ln x)^x*[ ln(ln(x))+1/ln(x)]
