e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
The first derivative of e to the x power is e to the power of x.
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
The derivative of ex is ex
d/dx (e-x) = -e-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
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
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.
Your expression simplifies to just x^2 {with the restriction that x > 0}. The derivative of x^2 is 2*x
d/dx (ex + x3) = ex + 3x2
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
2.71828183 ==So the derivative of a constant is zero.If you have e^x, the derivative is e^x.
The integral of (-e^x) with respect to (x) is (-e^x + C), where (C) is the constant of integration. This represents the family of functions whose derivative is (-e^x).