Mister Exam
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How to use it?
- Derivative of:
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Derivative of (x^2-x)*(x^3+x)
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Derivative of sqrt(x^2-1)
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Derivative of log(1+x)
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Derivative of sin(x)*tan(x)
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Identical expressions
- y=sh(ln(tg2x))
- y equally sh(ln(tg2x))
- y=shlntg2x
Derivative of y=sh(ln(tg2x))
The solution
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sinh(log(tan(2*x)))
$$\sinh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}$$
d --(sinh(log(tan(2*x)))) dx
$$\frac{d}{d x} \sinh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}$$
The first derivative
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/ 2 \
\2 + 2*tan (2*x)/*cosh(log(tan(2*x)))
-------------------------------------
tan(2*x)
$$\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \cosh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan{\left(2 x \right)}}$$
The second derivative
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/ / 2 \ / 2 \ \
/ 2 \ | \1 + tan (2*x)/*sinh(log(tan(2*x))) \1 + tan (2*x)/*cosh(log(tan(2*x)))|
4*\1 + tan (2*x)/*|2*cosh(log(tan(2*x))) + ----------------------------------- - -----------------------------------|
| 2 2 |
\ tan (2*x) tan (2*x) /
$$4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\frac{\left(\tan^{2}{\left(2 x \right)} + 1\right) \sinh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{\left(\tan^{2}{\left(2 x \right)} + 1\right) \cosh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan^{2}{\left(2 x \right)}} + 2 \cosh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}\right)$$
The third derivative
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/ 2 2 \
| / 2 \ / 2 \ / 2 \ / 2 \ |
/ 2 \ | 4*\1 + tan (2*x)/*cosh(log(tan(2*x))) 3*\1 + tan (2*x)/ *sinh(log(tan(2*x))) 3*\1 + tan (2*x)/ *cosh(log(tan(2*x))) 6*\1 + tan (2*x)/*sinh(log(tan(2*x)))|
8*\1 + tan (2*x)/*|4*cosh(log(tan(2*x)))*tan(2*x) - ------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------|
| tan(2*x) 3 3 tan(2*x) |
\ tan (2*x) tan (2*x) /
$$8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(- \frac{3 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \sinh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{3 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cosh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sinh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan{\left(2 x \right)}} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cosh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}}{\tan{\left(2 x \right)}} + 4 \tan{\left(2 x \right)} \cosh{\left(\log{\left(\tan{\left(2 x \right)} \right)} \right)}\right)$$
The graph