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 x^2+cos(x)
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Derivative of (x+1)^2*(x-5)-6
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Derivative of log(11*x)
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Derivative of e^x-2
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Identical expressions
- (sqrt(x))^sin^ two (x)
- ( square root of (x)) to the power of sinus of squared (x)
- ( square root of (x)) to the power of sinus of to the power of two (x)
- (√(x))^sin^2(x)
- (sqrt(x))sin2(x)
- sqrtxsin2x
- (sqrt(x))^sin²(x)
- (sqrt(x)) to the power of sin to the power of 2(x)
- sqrtx^sin^2x
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Similar expressions
- sqrt(x)^sin^2(x)
Derivative of (sqrt(x))^sin^2(x)
The solution
You have entered
[src]
2
sin (x)
___
\/ x
$$\left(\sqrt{x}\right)^{\sin^{2}{\left(x \right)}}$$
(sqrt(x))^(sin(x)^2)
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]
2
sin (x)
------- / 2 \
2 |sin (x) / ___\ |
x *|------- + 2*cos(x)*log\\/ x /*sin(x)|
\ 2*x /
$$x^{\frac{\sin^{2}{\left(x \right)}}{2}} \left(2 \log{\left(\sqrt{x} \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{2}{\left(x \right)}}{2 x}\right)$$
The second derivative
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2
sin (x) / 2 /sin(x) \ /sin(x) / ___\\\
------- | 2 sin (x)*|------ + 2*cos(x)*log(x)|*|------ + 4*cos(x)*log\\/ x /||
2 | 2 / ___\ 2 / ___\ sin (x) 2*cos(x)*sin(x) \ x / \ x /|
x *|- 2*sin (x)*log\\/ x / + 2*cos (x)*log\\/ x / - ------- + --------------- + -----------------------------------------------------------------|
| 2 x 4 |
\ 2*x /
$$x^{\frac{\sin^{2}{\left(x \right)}}{2}} \left(\frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{4} - 2 \log{\left(\sqrt{x} \right)} \sin^{2}{\left(x \right)} + 2 \log{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{\sin^{2}{\left(x \right)}}{2 x^{2}}\right)$$
The third derivative
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/ / 2 \ / 2 \ \
2 | /sin(x) \ |sin (x) 2 / ___\ 2 / ___\ 4*cos(x)*sin(x)| /sin(x) / ___\\ |sin (x) 2 2 4*cos(x)*sin(x)| 2 |
sin (x) | |------ + 2*cos(x)*log(x)|*|------- - 4*cos (x)*log\\/ x / + 4*sin (x)*log\\/ x / - ---------------|*sin(x) |------ + 4*cos(x)*log\\/ x /|*|------- - 2*cos (x)*log(x) + 2*sin (x)*log(x) - ---------------|*sin(x) /sin(x) \ 3 /sin(x) / ___\\|
------- | 2 2 2 \ x / | 2 x | \ x / | 2 x | |------ + 2*cos(x)*log(x)| *sin (x)*|------ + 4*cos(x)*log\\/ x /||
2 |sin (x) 3*sin (x) 3*cos (x) / ___\ 3*cos(x)*sin(x) \ x / \ x / \ x / \ x /|
x *|------- - --------- + --------- - 8*cos(x)*log\\/ x /*sin(x) - --------------- - ----------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------|
| 3 x x 2 2 4 8 |
\ x x /
$$x^{\frac{\sin^{2}{\left(x \right)}}{2}} \left(\frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{3}{\left(x \right)}}{8} - \frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(2 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 2 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{4} - \frac{\left(2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(4 \log{\left(\sqrt{x} \right)} \sin^{2}{\left(x \right)} - 4 \log{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} - \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{2} - 8 \log{\left(\sqrt{x} \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin^{2}{\left(x \right)}}{x} + \frac{3 \cos^{2}{\left(x \right)}}{x} - \frac{3 \sin{\left(x \right)} \cos{\left(x \right)}}{x^{2}} + \frac{\sin^{2}{\left(x \right)}}{x^{3}}\right)$$