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the number e is by definition the number which raised to x will produce a graph such that at every point on the graph the slope of the graph is equal to x.
In otherwords, the answer to your question is because that is the way e is defined.
IDK... I saw e^x defined as a power series.
Consider: Let y = e^x
Since x is real (by assumption) then
ln(y) = x, where ln(t) is the natural logarithm of t. Now differentiate with respect to x
1/y * (dy/dx) = 1 Multiplying both sides by y, we get
dy/dx = y = e^x. This fits with the first definition but is more rigorous.
What else can I help you with?
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 anti derivative of e raised to 6?
Well the number e, raised to 6 (e^6) is just a number (a constant), so you integrate a constant times dx gives you that constant times x + C --> x*e^6 + C
What is the derivative of e to the power of x?
The derivative of ex is ex
What is the derivative of -exp to the -x?
x e^x +C
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 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 -2 times x?
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
How can you prove that yis equal to e raise to the power xlny?
Euler's constant, e, has some basic rules when used in conjunction with logs. e raised to x?æln(y),?æby rule is equal to (e raised to ln(y) raised to x). e raised to ln (y) is equal to just y. Thus it becomes equal to y when x = 1 or 0.
E raised to the power of x equal 10?
It is possible.
What is the derivitive of e?
2.71828183 ==So the derivative of a constant is zero.If you have e^x, the derivative is e^x.
What is the anti derivative of e raised to 6?
Well the number e, raised to 6 (e^6) is just a number (a constant), so you integrate a constant times dx gives you that constant times x + C --> x*e^6 + C
What is the derivative of e negative x?
- e^- X
What is the derivative of e to the power of x?
The derivative of ex is ex
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 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
Anti-derivative of e-x?
I suppose you mean of e-x? It is -e-x + C.
What is the derivative of e power negative x?
d/dx (e-x) = -e-x
