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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
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of (5*x-4)*(2*x^4-7*x+1)
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Derivative of x/5+5/x
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Derivative of (x+5)^2*(x-1)+7
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Derivative of x^3-48x+17
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Identical expressions
- log^x*(x+ one)
- logarithm of to the power of x multiply by (x plus 1)
- logarithm of to the power of x multiply by (x plus one)
- logx*(x+1)
- logx*x+1
- log^x(x+1)
- logx(x+1)
- logxx+1
- log^xx+1
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Similar expressions
- log^x*(x-1)
Derivative of log^x*(x+1)
The solution
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
x / x \
log (x + 1)*|------------------ + log(log(x + 1))|
\(x + 1)*log(x + 1) /
$$\left(\frac{x}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \log{\left(\log{\left(x + 1 \right)} \right)}\right) \log{\left(x + 1 \right)}^{x}$$
The second derivative
[src]
/ x x \
| 2 -2 + ----- + ------------------|
x |/ x \ 1 + x (1 + x)*log(1 + x)|
log (1 + x)*||------------------ + log(log(1 + x))| - -------------------------------|
\\(1 + x)*log(1 + x) / (1 + x)*log(1 + x) /
$$\left(\left(\frac{x}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \log{\left(\log{\left(x + 1 \right)} \right)}\right)^{2} - \frac{\frac{x}{x + 1} + \frac{x}{\left(x + 1\right) \log{\left(x + 1 \right)}} - 2}{\left(x + 1\right) \log{\left(x + 1 \right)}}\right) \log{\left(x + 1 \right)}^{x}$$
The third derivative
[src]
/ 3 2*x 2*x 3*x \
| -3 - ---------- + ----- + ------------------- + ------------------ / x \ / x x \|
| 3 log(1 + x) 1 + x 2 (1 + x)*log(1 + x) 3*|------------------ + log(log(1 + x))|*|-2 + ----- + ------------------||
x |/ x \ (1 + x)*log (1 + x) \(1 + x)*log(1 + x) / \ 1 + x (1 + x)*log(1 + x)/|
log (1 + x)*||------------------ + log(log(1 + x))| + ------------------------------------------------------------------ - --------------------------------------------------------------------------|
|\(1 + x)*log(1 + x) / 2 (1 + x)*log(1 + x) |
\ (1 + x) *log(1 + x) /
$$\left(\left(\frac{x}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \log{\left(\log{\left(x + 1 \right)} \right)}\right)^{3} - \frac{3 \left(\frac{x}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \log{\left(\log{\left(x + 1 \right)} \right)}\right) \left(\frac{x}{x + 1} + \frac{x}{\left(x + 1\right) \log{\left(x + 1 \right)}} - 2\right)}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \frac{\frac{2 x}{x + 1} + \frac{3 x}{\left(x + 1\right) \log{\left(x + 1 \right)}} + \frac{2 x}{\left(x + 1\right) \log{\left(x + 1 \right)}^{2}} - 3 - \frac{3}{\log{\left(x + 1 \right)}}}{\left(x + 1\right)^{2} \log{\left(x + 1 \right)}}\right) \log{\left(x + 1 \right)}^{x}$$