Find the derivative of the following functions. ?

Question

Find the derivative of the following functions.

y = 2^x/e^x

f(x) = 2xln(x^ 2 + 5)

g(x) = ln x / e^(x^2+2)

Answer 1

f(x) = 2x ln(x^2 + 5)

f'(x) = u'v + uv'

f'(x) = 2 ln(x^2 + 5) + 2x (1/(x^2 + 5)) (2x)

f'(x) = 2 ln(x^2 + 5) + 4x^2 / (x^2 + 5)

Is it correct?

Thank you.

Answer 2

you use quotient rule for first and third and product rule for second. I hope you know all these rules. If not practice them first!

Answer 3

2^x*ln(2)/e^x-2^x*ln(e)/e^x

?

ln/e^(x^2+2)-2*ln*x^2*ln(e)/e^(x^2+2)