d/dx (ex + x3) = ex + 3x2
The first derivative of e to the x power is e to the power of x.
The derivative of ex is ex
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 derivative of xe is e. The derivative of xe is exe-1.
f'(x)=-3the derivative of e is zero because its a constant. Derivative of -3x is -3. Bring the exponent of x down in front of the -3 and subtract the original exponent by 1. Ex. -3(1...which is the first exponent of the x)x^0(n-1 or 1-1=0)all this is -3(1)x^0x^0 is 1 so the derivative of -3x is -3
The first derivative of e to the x power is e to the power of x.
The derivative of ex is ex
The anti-derivative of sqrt(x) : sqrt(x)=x^(1/2) The anti-derivative is x^(1/2+1) /(1/2+1) = (2/3) x^(3/2) The anti-derivative is 4e^x is 4 e^x ( I hope you meant e to the power x) The anti-derivative of -sin(x) is cos(x) Adding, the anti-derivative is (2/3) x^(3/2) + 4 e^x + cos(x) + C
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
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
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.
d/dx (e-x) = -e-x
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
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
If dy/dx = (e) (9x) then Y = 4.5ex2 plus (any constant).==================================The above answer explains how to get the integral of e9x.If you were interested in how to get the derivative of e9x, the answer is e9.I suspect you may have actually wanted to ask how to get the derivative of e9x.In that case, the derivative of e9x is 9e9x.
ee is a constant and so its derivative is 0.