Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of (x-2)^2
-
Derivative of e^-x
-
Derivative of (x-1)^2
-
Derivative of 1/sqrt(x)
-
Identical expressions
- y=sinh^ two (x/ two)+(one / two)coshx
- y equally hyperbolic sinus of e of squared (x divide by 2) plus (1 divide by 2) hyperbolic co sinus of e of ine of x
- y equally hyperbolic sinus of e of to the power of two (x divide by two) plus (one divide by two) hyperbolic co sinus of e of ine of x
- y=sinh2(x/2)+(1/2)coshx
- y=sinh2x/2+1/2coshx
- y=sinh²(x/2)+(1/2)coshx
- y=sinh to the power of 2(x/2)+(1/2)coshx
- y=sinh^2x/2+1/2coshx
- y=sinh^2(x divide by 2)+(1 divide by 2)coshx
-
Similar expressions
- y=(sinh^2)(x/2)+(1/2)coshx
- y=sinh^2(x/2)-(1/2)coshx
Derivative of y=sinh^2(x/2)+(1/2)coshx
The solution
You have entered
[src]
2/x\ cosh(x)
sinh |-| + -------
\2/ 2
$$\sinh^{2}{\left(\frac{x}{2} \right)} + \frac{\cosh{\left(x \right)}}{2}$$
sinh(x/2)^2 + cosh(x)/2
The first derivative
[src]
sinh(x) /x\ /x\ ------- + cosh|-|*sinh|-| 2 \2/ \2/
$$\frac{\sinh{\left(x \right)}}{2} + \sinh{\left(\frac{x}{2} \right)} \cosh{\left(\frac{x}{2} \right)}$$
The second derivative
[src]
2/x\ 2/x\
cosh |-| + sinh |-| + cosh(x)
\2/ \2/
-----------------------------
2
$$\frac{\sinh^{2}{\left(\frac{x}{2} \right)} + \cosh^{2}{\left(\frac{x}{2} \right)} + \cosh{\left(x \right)}}{2}$$
The third derivative
[src]
sinh(x) /x\ /x\ ------- + cosh|-|*sinh|-| 2 \2/ \2/
$$\sinh{\left(\frac{x}{2} \right)} \cosh{\left(\frac{x}{2} \right)} + \frac{\sinh{\left(x \right)}}{2}$$
The graph