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How to use it?
- Derivative of:
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Derivative of 8^x
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Derivative of 2*sinh(x)*cosh(x)
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Derivative of x^2*asinh(x)*acosh(x)
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Derivative of (x^2-4)/x
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Identical expressions
- eighteen *e^x/tanh(x)
- 18 multiply by e to the power of x divide by hyperbolic tangent of gent of (x)
- eighteen multiply by e to the power of x divide by hyperbolic tangent of gent of (x)
- 18*ex/tanh(x)
- 18*ex/tanhx
- 18e^x/tanh(x)
- 18ex/tanh(x)
- 18ex/tanhx
- 18e^x/tanhx
- 18*e^x divide by tanh(x)
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What you mean?
- 18*e^x/tanh(x)
- 18*e^x*x/tanh(x)
- 18*e^x/tanh(x)
- 18*e^x*x/tanh(x)
- 18*e*x/tanh(x)
- 18*e*x*x/tanh(x)
- 18*e^x*x/tanh(x)
You entered:
18*e^x/tanh(x)
What you mean?
Derivative of 18*e^x/tanh(x)
The solution
You have entered
[src]
x 18*e ------- tanh(x)
$$\frac{18 e^{x}}{\tanh{\left(x \right)}}$$
/ x \ d | 18*e | --|-------| dx\tanh(x)/
$$\frac{d}{d x} \frac{18 e^{x}}{\tanh{\left(x \right)}}$$
The first derivative
[src]
x / 2 \ x
18*e 18*\-1 + tanh (x)/*e
------- + ---------------------
tanh(x) 2
tanh (x)
$$\frac{18 \left(\tanh^{2}{\left(x \right)} - 1\right) e^{x}}{\tanh^{2}{\left(x \right)}} + \frac{18 e^{x}}{\tanh{\left(x \right)}}$$
The second derivative
[src]
/ / 2 \ / 2 \\
| 2*\-1 + tanh (x)/ / 2 \ | -1 + tanh (x)|| x
18*|1 + ----------------- + 2*\-1 + tanh (x)/*|-1 + -------------||*e
| tanh(x) | 2 ||
\ \ tanh (x) //
----------------------------------------------------------------------
tanh(x)
$$\frac{18 \cdot \left(2 \left(\frac{\tanh^{2}{\left(x \right)} - 1}{\tanh^{2}{\left(x \right)}} - 1\right) \left(\tanh^{2}{\left(x \right)} - 1\right) + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh{\left(x \right)}} + 1\right) e^{x}}{\tanh{\left(x \right)}}$$
The third derivative
[src]
/ / 2 \\ | / 2 \ | -1 + tanh (x)|| | 2 3 6*\-1 + tanh (x)/*|-1 + -------------|| | / 2 \ / 2 \ / 2 \ | 2 || | 1 2 10*\-1 + tanh (x)/ 3*\-1 + tanh (x)/ 6*\-1 + tanh (x)/ \ tanh (x) /| x 18*|-4 + ------- + 4*tanh (x) - ------------------- + ----------------- + ------------------ + --------------------------------------|*e | tanh(x) 2 2 4 tanh(x) | \ tanh (x) tanh (x) tanh (x) /
$$18 \cdot \left(\frac{6 \left(\frac{\tanh^{2}{\left(x \right)} - 1}{\tanh^{2}{\left(x \right)}} - 1\right) \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh{\left(x \right)}} + \frac{6 \left(\tanh^{2}{\left(x \right)} - 1\right)^{3}}{\tanh^{4}{\left(x \right)}} - \frac{10 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2}}{\tanh^{2}{\left(x \right)}} + \frac{3 \left(\tanh^{2}{\left(x \right)} - 1\right)}{\tanh^{2}{\left(x \right)}} + 4 \tanh^{2}{\left(x \right)} - 4 + \frac{1}{\tanh{\left(x \right)}}\right) e^{x}$$
The graph