Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of x^e
-
Derivative of (x^3-1)(x^2+x+1)
-
Derivative of e^(sin(1-3*x)^(2))
-
Derivative of -3*x^3+2*x^2-x-5
- Integral of d{x}:
-
x^e
- Limit of the function:
-
x^e
-
Identical expressions
- x^e
- x to the power of e
- xe
-
Similar expressions
- y=x^(e^ctg(x))
- (cos(5x))^e^x
Derivative of x^e
The solution
Detail solution
-
Apply the power rule: goes to
-
Now simplify:
The answer is:
The second derivative
[src]
E
E*x *(-1 + E)
-------------
2
x
$$\frac{e x^{e} \left(-1 + e\right)}{x^{2}}$$
The third derivative
[src]
E / 2\
E*x *\2 - 3*E + e /
-------------------
3
x
$$\frac{e x^{e} \left(- 3 e + 2 + e^{2}\right)}{x^{3}}$$
The graph