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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 1/x^6
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Derivative of x+lnx
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Derivative of x^2-4*x+3
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Derivative of -(x^2+324)/x
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Identical expressions
- y=x^cosh(x)
- y equally x to the power of hyperbolic co sinus of e of ine of (x)
- y=xcosh(x)
- y=xcoshx
- y=x^coshx
Derivative of y=x^cosh(x)
The solution
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
cosh(x) /cosh(x) \
x *|------- + log(x)*sinh(x)|
\ x /
$$x^{\cosh{\left(x \right)}} \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)$$
The second derivative
[src]
/ 2 \
cosh(x) |/cosh(x) \ cosh(x) 2*sinh(x)|
x *||------- + log(x)*sinh(x)| + cosh(x)*log(x) - ------- + ---------|
|\ x / 2 x |
\ x /
$$x^{\cosh{\left(x \right)}} \left(\left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)^{2} + \log{\left(x \right)} \cosh{\left(x \right)} + \frac{2 \sinh{\left(x \right)}}{x} - \frac{\cosh{\left(x \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 \
cosh(x) |/cosh(x) \ 3*sinh(x) 2*cosh(x) 3*cosh(x) /cosh(x) \ / cosh(x) 2*sinh(x)\|
x *||------- + log(x)*sinh(x)| + log(x)*sinh(x) - --------- + --------- + --------- + 3*|------- + log(x)*sinh(x)|*|cosh(x)*log(x) - ------- + ---------||
|\ x / 2 3 x \ x / | 2 x ||
\ x x \ x //
$$x^{\cosh{\left(x \right)}} \left(\left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{2 \sinh{\left(x \right)}}{x} - \frac{\cosh{\left(x \right)}}{x^{2}}\right) + \log{\left(x \right)} \sinh{\left(x \right)} + \frac{3 \cosh{\left(x \right)}}{x} - \frac{3 \sinh{\left(x \right)}}{x^{2}} + \frac{2 \cosh{\left(x \right)}}{x^{3}}\right)$$