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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of y=x^4•logx
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Derivative of y=ln(coshx)
- Derivative of y'=asinx+bcosx
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Derivative of y=sin^4(2x)
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Identical expressions
- y=ln(coshx)
- y equally ln( hyperbolic co sinus of e of ine of x)
- y=lncoshx
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Similar expressions
- y=lncosh(x)
- y=lncoshx
- y=ln(cosh(x))
Derivative of y=ln(coshx)
The solution
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log(cosh(x))
$$\log{\left(\cosh{\left(x \right)} \right)}$$
d --(log(cosh(x))) dx
$$\frac{d}{d x} \log{\left(\cosh{\left(x \right)} \right)}$$
The first derivative
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sinh(x) ------- cosh(x)
$$\frac{\sinh{\left(x \right)}}{\cosh{\left(x \right)}}$$
The second derivative
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2
sinh (x)
1 - --------
2
cosh (x)
$$- \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + 1$$
The third derivative
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/ 2 \
| sinh (x)|
2*|-1 + --------|*sinh(x)
| 2 |
\ cosh (x)/
-------------------------
cosh(x)
$$\frac{2 \left(\frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 1\right) \sinh{\left(x \right)}}{\cosh{\left(x \right)}}$$
The graph