- #1
lamerali
- 62
- 0
Hi, I'm working with finding the derivatives of functions, which I'm not very comfortable with; if someone could please check my answers to the following questions i would be VERY grateful! Thank you! :)
find the derivative of the following function:
Question 1:
y = [tex]\frac{ 2^{x} }{ e^{x} }[/tex]
My Answer
y1 = [tex]\frac{ e^{x} . ln2 . 2^{x} + 2^{x} . e^{x} }{ e^{x}^{2} }[/tex]
= [tex]\frac{ 2^{x} (ln2 + 1) }{ e^{x} }[/tex]
Question 2:
f(x) = 2x ln(x[tex]^{2}[/tex] + 5)
My answer
f [tex]^{1}[/tex] (x) = 2ln(x[tex]^{2}[/tex] + 5) + (2x) . [tex]\frac{1}{x^{2} + 5}[/tex] . (2x)
= 2 ln(x[tex]^{2}[/tex] + 5) + [tex]\frac{4x^{2}}{x^{2} + 5}[/tex]
Question 3:
g(x) = [tex]\frac{ln x}{e^{x}^{2} + 2}[/tex]
My answer:
g[tex]^{1}[/tex](x) = [tex]\frac{(e^{x}^{2} + 2) . (1/x) - lnx . 2xe^{x}^{2}}{(e^{x}^{2} + 2)^{2}}[/tex]
= [tex]\frac{\frac{e^{x}^{2} + 2}{x} - lnx . 2xe^{x}^{2}}{(e^{x}^{2} + 2)^{2}}[/tex]
for the last two questions I'm not sure if i simplified enough...if anyone could guide me in the right direction where needed i'd really appreciate it! thanks in advance!
find the derivative of the following function:
Question 1:
y = [tex]\frac{ 2^{x} }{ e^{x} }[/tex]
My Answer
y1 = [tex]\frac{ e^{x} . ln2 . 2^{x} + 2^{x} . e^{x} }{ e^{x}^{2} }[/tex]
= [tex]\frac{ 2^{x} (ln2 + 1) }{ e^{x} }[/tex]
Question 2:
f(x) = 2x ln(x[tex]^{2}[/tex] + 5)
My answer
f [tex]^{1}[/tex] (x) = 2ln(x[tex]^{2}[/tex] + 5) + (2x) . [tex]\frac{1}{x^{2} + 5}[/tex] . (2x)
= 2 ln(x[tex]^{2}[/tex] + 5) + [tex]\frac{4x^{2}}{x^{2} + 5}[/tex]
Question 3:
g(x) = [tex]\frac{ln x}{e^{x}^{2} + 2}[/tex]
My answer:
g[tex]^{1}[/tex](x) = [tex]\frac{(e^{x}^{2} + 2) . (1/x) - lnx . 2xe^{x}^{2}}{(e^{x}^{2} + 2)^{2}}[/tex]
= [tex]\frac{\frac{e^{x}^{2} + 2}{x} - lnx . 2xe^{x}^{2}}{(e^{x}^{2} + 2)^{2}}[/tex]
for the last two questions I'm not sure if i simplified enough...if anyone could guide me in the right direction where needed i'd really appreciate it! thanks in advance!