0
f(x) = (x^2)(e^x)
f'(x) = e^x((x^2)+2x) - i think
f"(x) = ?
--------
f(x) = (x^2)(e^x)
apply the power rule
f'(x) = (x^2)(e^x) + (2x)(e^x)
apply the power rule to the first part and apply the power rule to the second part, then add those together
f''(x) = [(x^2)(e^x) + (2x)(e^x)] + [(2x)(e^x) + (2)(e^x)]
simplify
f''(x) = (e^x)(x^2 + 4x +2)
I got it right. It checked out on my calculator.
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Fran
TaigaAdd your answer:
Earn +20 pts
How do you differentiate exponential function?
The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
Differentiate log x?
The derivative of ln x, the natural logarithm, is 1/x.Otherwise, given the identity logbx = log(x)/log(b), we know that the derivative of logbx = 1/(x*log b).ProofThe derivative of ln x follows quickly once we know that the derivative of ex is itself. Let y = ln x (we're interested in knowing dy/dx)Then ey = xDifferentiate both sides to get ey dy/dx = 1Substitute ey = x to get x dy/dx = 1, or dy/dx = 1/x.Differentiation of log (base 10) xlog (base 10) x= log (base e) x * log (base 10) ed/dx [ log (base 10) x ]= d/dx [ log (base e) x * log (base 10) e ]= [log(base 10) e] / x= 1 / x ln(10)
How do you integrate x power x?
e^x/1-e^x
E raised to the power of x equal 10?
It is possible.
What is 10000000 to the power of 10?
10,000,00010 = 1.e+70
