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How to use it?
- Derivative of:
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Derivative of f(x)=x^2
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Derivative of x×ln(x)
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Derivative of x^4+4*x^3-8*x^2-5
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Derivative of -(x^2+289)/x
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Identical expressions
- y=x^2lnsinhx
- y equally x squared ln hyperbolic sinus of e of x
- y=x2lnsinhx
- y=x²lnsinhx
- y=x to the power of 2lnsinhx
Derivative of y=x^2lnsinhx
The solution
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2 x *log(sinh(x))
$$x^{2} \log{\left(\sinh{\left(x \right)} \right)}$$
d / 2 \ --\x *log(sinh(x))/ dx
$$\frac{d}{d x} x^{2} \log{\left(\sinh{\left(x \right)} \right)}$$
The first derivative
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2
x *cosh(x)
2*x*log(sinh(x)) + ----------
sinh(x)
$$\frac{x^{2} \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 x \log{\left(\sinh{\left(x \right)} \right)}$$
The second derivative
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/ 2 \
2 | cosh (x)| 4*x*cosh(x)
2*log(sinh(x)) + x *|1 - --------| + -----------
| 2 | sinh(x)
\ sinh (x)/
$$x^{2} \cdot \left(1 - \frac{\cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) + \frac{4 x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}$$
The third derivative
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/ / 2 \ \ | 2 | cosh (x)| | | x *|1 - --------|*cosh(x)| | / 2 \ | 2 | | | | cosh (x)| 3*cosh(x) \ sinh (x)/ | 2*|3*x*|1 - --------| + --------- - -------------------------| | | 2 | sinh(x) sinh(x) | \ \ sinh (x)/ /
$$2 \left(- \frac{x^{2} \cdot \left(1 - \frac{\cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 3 x \left(1 - \frac{\cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) + \frac{3 \cosh{\left(x \right)}}{\sinh{\left(x \right)}}\right)$$
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