Mister Exam
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- 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
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How to use it?
- Derivative of:
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Derivative of tan(t)
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Derivative of log(x^2+5)
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Derivative of e^x*sinx
- Derivative of i*n*sin(x)
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Identical expressions
- y=sinx^(sinx)
- y equally sinus of x to the power of ( sinus of x)
- y=sinx(sinx)
- y=sinxsinx
- y=sinx^sinx
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Similar expressions
- y=sinx^sinx
Derivative of y=sinx^(sinx)
The solution
You have entered
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sin(x) sin (x)
$$\sin^{\sin{\left(x \right)}}{\left(x \right)}$$
d / sin(x) \ --\sin (x)/ dx
$$\frac{d}{d x} \sin^{\sin{\left(x \right)}}{\left(x \right)}$$
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
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sin(x) sin (x)*(cos(x)*log(sin(x)) + cos(x))
$$\left(\log{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)} + \cos{\left(x \right)}\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}$$
The second derivative
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/ 2 \
sin(x) | 2 2 cos (x) |
sin (x)*|-sin(x) + (1 + log(sin(x))) *cos (x) + ------- - log(sin(x))*sin(x)|
\ sin(x) /
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right)^{2} \cos^{2}{\left(x \right)} - \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}$$
The third derivative
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/ 2 / 2 \\
sin(x) | 3 2 cos (x) | cos (x) ||
sin (x)*|-4 - log(sin(x)) + (1 + log(sin(x))) *cos (x) - ------- - 3*(1 + log(sin(x)))*|log(sin(x))*sin(x) - ------- + sin(x)||*cos(x)
| 2 \ sin(x) /|
\ sin (x) /
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right)^{3} \cos^{2}{\left(x \right)} - 3 \left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) - \log{\left(\sin{\left(x \right)} \right)} - 4 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\sin{\left(x \right)}}{\left(x \right)} \cos{\left(x \right)}$$
The graph