Mister Exam
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- 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
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How to use it?
- Derivative of:
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Derivative of (-6)/x^4
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Derivative of y=√4-x^2
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Derivative of x^(x^2+1)
- Derivative of loga^x
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Identical expressions
- x^(x^ two + one)
- x to the power of (x squared plus 1)
- x to the power of (x to the power of two plus one)
- x(x2+1)
- xx2+1
- x^(x²+1)
- x to the power of (x to the power of 2+1)
- x^x^2+1
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Similar expressions
- x^(x^2-1)
Derivative of x^(x^2+1)
The solution
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
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Now simplify:
The answer is:
The first derivative
[src]
2 / 2 \
x + 1 |x + 1 |
x *|------ + 2*x*log(x)|
\ x /
$$x^{x^{2} + 1} \left(2 x \log{\left(x \right)} + \frac{x^{2} + 1}{x}\right)$$
The second derivative
[src]
/ 2 \
2 | / 2 \ 2|
1 + x | |1 + x | 1 + x |
x *|4 + |------ + 2*x*log(x)| + 2*log(x) - ------|
| \ x / 2 |
\ x /
$$x^{x^{2} + 1} \left(\left(2 x \log{\left(x \right)} + \frac{x^{2} + 1}{x}\right)^{2} + 2 \log{\left(x \right)} + 4 - \frac{x^{2} + 1}{x^{2}}\right)$$
The third derivative
[src]
/ 3 \
2 |/ 2 \ / 2\ / 2 \ / 2\|
1 + x ||1 + x | 2*\1 + x / |1 + x | | 1 + x ||
x *||------ + 2*x*log(x)| + ---------- + 3*|------ + 2*x*log(x)|*|4 + 2*log(x) - ------||
|\ x / 3 \ x / | 2 ||
\ x \ x //
$$x^{x^{2} + 1} \left(\left(2 x \log{\left(x \right)} + \frac{x^{2} + 1}{x}\right)^{3} + 3 \left(2 x \log{\left(x \right)} + \frac{x^{2} + 1}{x}\right) \left(2 \log{\left(x \right)} + 4 - \frac{x^{2} + 1}{x^{2}}\right) + \frac{2 \left(x^{2} + 1\right)}{x^{3}}\right)$$
The graph