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How to use it?
- Derivative of:
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Derivative of x^(3/4)
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Derivative of (x^2-2)*(x^7+4)
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Derivative of (x-1)
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Derivative of sqrt(x^3)
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Identical expressions
- (x+ two ^x)^ln(x)
- (x plus 2 to the power of x) to the power of ln(x)
- (x plus two to the power of x) to the power of ln(x)
- (x+2x)ln(x)
- x+2xlnx
- x+2^x^lnx
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Similar expressions
- (x-2^x)^ln(x)
Derivative of (x+2^x)^ln(x)
The solution
You have entered
[src]
log(x) / x\ \x + 2 /
$$\left(2^{x} + x\right)^{\log{\left(x \right)}}$$
(x + 2^x)^log(x)
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]
log(x) / / x\ / x \ \
/ x\ |log\x + 2 / \1 + 2 *log(2)/*log(x)|
\x + 2 / *|----------- + ----------------------|
| x x |
\ x + 2 /
$$\left(2^{x} + x\right)^{\log{\left(x \right)}} \left(\frac{\left(2^{x} \log{\left(2 \right)} + 1\right) \log{\left(x \right)}}{2^{x} + x} + \frac{\log{\left(2^{x} + x \right)}}{x}\right)$$
The second derivative
[src]
/ 2 2 \
log(x) |/ / x\ / x \ \ / x\ / x \ / x \ x 2 |
/ x\ ||log\x + 2 / \1 + 2 *log(2)/*log(x)| log\x + 2 / \1 + 2 *log(2)/ *log(x) 2*\1 + 2 *log(2)/ 2 *log (2)*log(x)|
\x + 2 / *||----------- + ----------------------| - ----------- - ----------------------- + ----------------- + -----------------|
|| x x | 2 2 / x\ x |
|\ x + 2 / x / x\ x*\x + 2 / x + 2 |
\ \x + 2 / /
$$\left(2^{x} + x\right)^{\log{\left(x \right)}} \left(\frac{2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)}}{2^{x} + x} + \left(\frac{\left(2^{x} \log{\left(2 \right)} + 1\right) \log{\left(x \right)}}{2^{x} + x} + \frac{\log{\left(2^{x} + x \right)}}{x}\right)^{2} - \frac{\left(2^{x} \log{\left(2 \right)} + 1\right)^{2} \log{\left(x \right)}}{\left(2^{x} + x\right)^{2}} + \frac{2 \left(2^{x} \log{\left(2 \right)} + 1\right)}{x \left(2^{x} + x\right)} - \frac{\log{\left(2^{x} + x \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 / 2 \ 2 3 \
log(x) |/ / x\ / x \ \ / x\ / / x\ / x \ \ | / x\ / x \ / x \ x 2 | / x \ / x \ / x \ x 3 x 2 x 2 / x \ |
/ x\ ||log\x + 2 / \1 + 2 *log(2)/*log(x)| 2*log\x + 2 / |log\x + 2 / \1 + 2 *log(2)/*log(x)| | log\x + 2 / \1 + 2 *log(2)/ *log(x) 2*\1 + 2 *log(2)/ 2 *log (2)*log(x)| 3*\1 + 2 *log(2)/ 3*\1 + 2 *log(2)/ 2*\1 + 2 *log(2)/ *log(x) 2 *log (2)*log(x) 3*2 *log (2) 3*2 *log (2)*\1 + 2 *log(2)/*log(x)|
\x + 2 / *||----------- + ----------------------| + ------------- + 3*|----------- + ----------------------|*|- ----------- - ----------------------- + ----------------- + -----------------| - ------------------ - ----------------- + ------------------------- + ----------------- + ------------ - -----------------------------------|
|| x x | 3 | x x | | 2 2 / x\ x | 2 2 / x\ 3 x / x\ 2 |
|\ x + 2 / x \ x + 2 / | x / x\ x*\x + 2 / x + 2 | / x\ x *\x + 2 / / x\ x + 2 x*\x + 2 / / x\ |
\ \ \x + 2 / / x*\x + 2 / \x + 2 / \x + 2 / /
$$\left(2^{x} + x\right)^{\log{\left(x \right)}} \left(\frac{2^{x} \log{\left(2 \right)}^{3} \log{\left(x \right)}}{2^{x} + x} - \frac{3 \cdot 2^{x} \left(2^{x} \log{\left(2 \right)} + 1\right) \log{\left(2 \right)}^{2} \log{\left(x \right)}}{\left(2^{x} + x\right)^{2}} + \frac{3 \cdot 2^{x} \log{\left(2 \right)}^{2}}{x \left(2^{x} + x\right)} + \left(\frac{\left(2^{x} \log{\left(2 \right)} + 1\right) \log{\left(x \right)}}{2^{x} + x} + \frac{\log{\left(2^{x} + x \right)}}{x}\right)^{3} + 3 \left(\frac{\left(2^{x} \log{\left(2 \right)} + 1\right) \log{\left(x \right)}}{2^{x} + x} + \frac{\log{\left(2^{x} + x \right)}}{x}\right) \left(\frac{2^{x} \log{\left(2 \right)}^{2} \log{\left(x \right)}}{2^{x} + x} - \frac{\left(2^{x} \log{\left(2 \right)} + 1\right)^{2} \log{\left(x \right)}}{\left(2^{x} + x\right)^{2}} + \frac{2 \left(2^{x} \log{\left(2 \right)} + 1\right)}{x \left(2^{x} + x\right)} - \frac{\log{\left(2^{x} + x \right)}}{x^{2}}\right) + \frac{2 \left(2^{x} \log{\left(2 \right)} + 1\right)^{3} \log{\left(x \right)}}{\left(2^{x} + x\right)^{3}} - \frac{3 \left(2^{x} \log{\left(2 \right)} + 1\right)^{2}}{x \left(2^{x} + x\right)^{2}} - \frac{3 \left(2^{x} \log{\left(2 \right)} + 1\right)}{x^{2} \left(2^{x} + x\right)} + \frac{2 \log{\left(2^{x} + x \right)}}{x^{3}}\right)$$
The graph