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.
What else can I help you with?
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
What is the first derivative of e raised to the power of x?
The first derivative of e to the x power is e to the power of x.
What is the derivative of e to the power of x?
The derivative of ex is ex
What is the derivative of e to the power of -2 times x?
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
What is Y double-prime plus y equals 0?
y"+y'=0 is a differential equation and mean the first derivative plus the second derivative =0.Look at e-x the first derivative is -e-xThe second derivative will be e-xThe sum will be 0
How do you do derivative 27ex?
I assume you mean 27 times e to the power x. 1) You take out the constant out. So, the derivative is 27 times the derivative of (e to the power x).2) You use the rule for the exponential function.
What is the derivative of e power negative x?
d/dx (e-x) = -e-x
What is the derivative of x to the power of e?
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
What is the derivative of e to the power ln x squared?
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
What is the derivative of e the the power ln x?
y = e^ln x using the fact that e to the ln x is just x, and the derivative of x is 1: y = x y' = 1
What is the derivative of e to the e?
ee is a constant and so its derivative is 0.
What is the derivative of e to the power of 2lnx?
Your expression simplifies to just x^2 {with the restriction that x > 0}. The derivative of x^2 is 2*x
What is the physical application of third- and fourth-order derivatives with respect to distance e g first derivative is slope?
in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk
