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^3+2*x^5
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Derivative of (3*x-5)^6
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Derivative of 1/3*x^3-4*x
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Derivative of x²-4
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Identical expressions
- tg(x)^(x- one)
- tg(x) to the power of (x minus 1)
- tg(x) to the power of (x minus one)
- tg(x)(x-1)
- tgxx-1
- tgx^x-1
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Similar expressions
- tg(x)^(x+1)
Derivative of tg(x)^(x-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 \ \
x - 1 |\1 + tan (x)/*(x - 1) |
tan (x)*|--------------------- + log(tan(x))|
\ tan(x) /
$$\left(\frac{\left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{x - 1}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
|// 2 \ \ / / 2 \ \|
-1 + x ||\1 + tan (x)/*(-1 + x) | / 2 \ | 2 \1 + tan (x)/*(-1 + x)||
tan (x)*||---------------------- + log(tan(x))| + \1 + tan (x)/*|-2 + 2*x + ------ - ----------------------||
|\ tan(x) / | tan(x) 2 ||
\ \ tan (x) //
$$\left(\left(\frac{\left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{2} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} - 2 + \frac{2}{\tan{\left(x \right)}}\right)\right) \tan^{x - 1}{\left(x \right)}$$
The third derivative
[src]
/ 3 2 2 3 \
| // 2 \ \ / 2 \ / 2 \ / 2 \ // 2 \ \ / / 2 \ \ |
-1 + x | |\1 + tan (x)/*(-1 + x) | 2 3*\1 + tan (x)/ 4*\1 + tan (x)/ *(-1 + x) 2*\1 + tan (x)/ *(-1 + x) / 2 \ |\1 + tan (x)/*(-1 + x) | | 2 \1 + tan (x)/*(-1 + x)| / 2 \ |
tan (x)*|6 + |---------------------- + log(tan(x))| + 6*tan (x) - ---------------- - ------------------------- + ------------------------- + 3*\1 + tan (x)/*|---------------------- + log(tan(x))|*|-2 + 2*x + ------ - ----------------------| + 4*\1 + tan (x)/*(-1 + x)*tan(x)|
| \ tan(x) / 2 tan(x) 3 \ tan(x) / | tan(x) 2 | |
\ tan (x) tan (x) \ tan (x) / /
$$\left(\frac{2 \left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 4 \left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \left(\frac{\left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{\left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} - 2 + \frac{2}{\tan{\left(x \right)}}\right) - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 6 \tan^{2}{\left(x \right)} + 6\right) \tan^{x - 1}{\left(x \right)}$$