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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
- Derivative of x|x|
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Derivative of (2*x+3)*e^(3*x)
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Derivative of y=x^3+2x^2+3x+4
- Derivative of x/(x^2+a^2)^(3/2)
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Identical expressions
- y=x^sinhx
- y equally x to the power of hyperbolic sinus of e of x
- y=xsinhx
Derivative of y=x^sinhx
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]
sinh(x) /sinh(x) \
x *|------- + cosh(x)*log(x)|
\ x /
$$x^{\sinh{\left(x \right)}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right)$$
The second derivative
[src]
/ 2 \
sinh(x) |/sinh(x) \ sinh(x) 2*cosh(x)|
x *||------- + cosh(x)*log(x)| + log(x)*sinh(x) - ------- + ---------|
|\ x / 2 x |
\ x /
$$x^{\sinh{\left(x \right)}} \left(\left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right)^{2} + \log{\left(x \right)} \sinh{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{\sinh{\left(x \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 \
sinh(x) |/sinh(x) \ 3*cosh(x) 2*sinh(x) 3*sinh(x) /sinh(x) \ / sinh(x) 2*cosh(x)\|
x *||------- + cosh(x)*log(x)| + cosh(x)*log(x) - --------- + --------- + --------- + 3*|------- + cosh(x)*log(x)|*|log(x)*sinh(x) - ------- + ---------||
|\ x / 2 3 x \ x / | 2 x ||
\ x x \ x //
$$x^{\sinh{\left(x \right)}} \left(\left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{\sinh{\left(x \right)}}{x^{2}}\right) + \log{\left(x \right)} \cosh{\left(x \right)} + \frac{3 \sinh{\left(x \right)}}{x} - \frac{3 \cosh{\left(x \right)}}{x^{2}} + \frac{2 \sinh{\left(x \right)}}{x^{3}}\right)$$