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
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How to use it?
- Derivative of:
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Derivative of (x^5+1)
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Derivative of x^sqrt(x)
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Derivative of log(x+2)
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Derivative of ex^2
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Identical expressions
- (log(x))^(three ^x)
- ( logarithm of (x)) to the power of (3 to the power of x)
- ( logarithm of (x)) to the power of (three to the power of x)
- (log(x))(3x)
- logx3x
- logx^3^x
Derivative of (log(x))^(3^x)
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]
/ x\ / x \
\3 / | 3 x |
(log(x)) *|-------- + 3 *log(3)*log(log(x))|
\x*log(x) /
$$\left(3^{x} \log{\left(3 \right)} \log{\left(\log{\left(x \right)} \right)} + \frac{3^{x}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{3^{x}}$$
The second derivative
[src]
/ x\ / 2 \
x \3 / | x / 1 \ 2 1 1 2*log(3)|
3 *(log(x)) *|3 *|-------- + log(3)*log(log(x))| + log (3)*log(log(x)) - --------- - ---------- + --------|
| \x*log(x) / 2 2 2 x*log(x)|
\ x *log(x) x *log (x) /
$$3^{x} \left(3^{x} \left(\log{\left(3 \right)} \log{\left(\log{\left(x \right)} \right)} + \frac{1}{x \log{\left(x \right)}}\right)^{2} + \log{\left(3 \right)}^{2} \log{\left(\log{\left(x \right)} \right)} + \frac{2 \log{\left(3 \right)}}{x \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{3^{x}}$$
The third derivative
[src]
/ x\ / 3 2 \
x \3 / | 2*x / 1 \ 3 2 2 3 3*log(3) 3*log(3) x / 1 \ / 2 1 1 2*log(3)\ 3*log (3)|
3 *(log(x)) *|3 *|-------- + log(3)*log(log(x))| + log (3)*log(log(x)) + --------- + ---------- + ---------- - --------- - ---------- + 3*3 *|-------- + log(3)*log(log(x))|*|log (3)*log(log(x)) - --------- - ---------- + --------| + ---------|
| \x*log(x) / 3 3 3 3 2 2 2 2 \x*log(x) / | 2 2 2 x*log(x)| x*log(x)|
\ x *log(x) x *log (x) x *log (x) x *log(x) x *log (x) \ x *log(x) x *log (x) / /
$$3^{x} \left(3^{2 x} \left(\log{\left(3 \right)} \log{\left(\log{\left(x \right)} \right)} + \frac{1}{x \log{\left(x \right)}}\right)^{3} + 3 \cdot 3^{x} \left(\log{\left(3 \right)} \log{\left(\log{\left(x \right)} \right)} + \frac{1}{x \log{\left(x \right)}}\right) \left(\log{\left(3 \right)}^{2} \log{\left(\log{\left(x \right)} \right)} + \frac{2 \log{\left(3 \right)}}{x \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}} - \frac{1}{x^{2} \log{\left(x \right)}^{2}}\right) + \log{\left(3 \right)}^{3} \log{\left(\log{\left(x \right)} \right)} + \frac{3 \log{\left(3 \right)}^{2}}{x \log{\left(x \right)}} - \frac{3 \log{\left(3 \right)}}{x^{2} \log{\left(x \right)}} - \frac{3 \log{\left(3 \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2}{x^{3} \log{\left(x \right)}} + \frac{3}{x^{3} \log{\left(x \right)}^{2}} + \frac{2}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{3^{x}}$$