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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of 8lnx
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Derivative of x^3-x+3
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Derivative of x^3/(2(x+1)^2)
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Derivative of x²-2x+1
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Identical expressions
- (x- two)^(sinx^ two)
- (x minus 2) to the power of ( sinus of x squared )
- (x minus two) to the power of ( sinus of x to the power of two)
- (x-2)(sinx2)
- x-2sinx2
- (x-2)^(sinx²)
- (x-2) to the power of (sinx to the power of 2)
- x-2^sinx^2
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Similar expressions
- (x+2)^(sinx^2)
Derivative of (x-2)^(sinx^2)
The solution
You have entered
[src]
2
sin (x)
(x - 2)
$$\left(x - 2\right)^{\sin^{2}{\left(x \right)}}$$
(x - 2)^(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 / 2 \
sin (x) |sin (x) |
(x - 2) *|------- + 2*cos(x)*log(x - 2)*sin(x)|
\ x - 2 /
$$\left(x - 2\right)^{\sin^{2}{\left(x \right)}} \left(2 \log{\left(x - 2 \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{2}{\left(x \right)}}{x - 2}\right)$$
The second derivative
[src]
2 / 2 2 \
sin (x) |/sin(x) \ 2 sin (x) 2 2 4*cos(x)*sin(x)|
(-2 + x) *||------ + 2*cos(x)*log(-2 + x)| *sin (x) - --------- - 2*sin (x)*log(-2 + x) + 2*cos (x)*log(-2 + x) + ---------------|
|\-2 + x / 2 -2 + x |
\ (-2 + x) /
$$\left(x - 2\right)^{\sin^{2}{\left(x \right)}} \left(\left(2 \log{\left(x - 2 \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x - 2}\right)^{2} \sin^{2}{\left(x \right)} - 2 \log{\left(x - 2 \right)} \sin^{2}{\left(x \right)} + 2 \log{\left(x - 2 \right)} \cos^{2}{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x - 2} - \frac{\sin^{2}{\left(x \right)}}{\left(x - 2\right)^{2}}\right)$$
The third derivative
[src]
2 / 3 2 2 2 / 2 \ \
sin (x) |/sin(x) \ 3 6*sin (x) 2*sin (x) 6*cos (x) 6*cos(x)*sin(x) /sin(x) \ | sin (x) 2 2 4*cos(x)*sin(x)| |
(-2 + x) *||------ + 2*cos(x)*log(-2 + x)| *sin (x) - --------- + --------- + --------- - 8*cos(x)*log(-2 + x)*sin(x) - --------------- - 3*|------ + 2*cos(x)*log(-2 + x)|*|--------- - 2*cos (x)*log(-2 + x) + 2*sin (x)*log(-2 + x) - ---------------|*sin(x)|
|\-2 + x / -2 + x 3 -2 + x 2 \-2 + x / | 2 -2 + x | |
\ (-2 + x) (-2 + x) \(-2 + x) / /
$$\left(x - 2\right)^{\sin^{2}{\left(x \right)}} \left(\left(2 \log{\left(x - 2 \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x - 2}\right)^{3} \sin^{3}{\left(x \right)} - 3 \left(2 \log{\left(x - 2 \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x - 2}\right) \left(2 \log{\left(x - 2 \right)} \sin^{2}{\left(x \right)} - 2 \log{\left(x - 2 \right)} \cos^{2}{\left(x \right)} - \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x - 2} + \frac{\sin^{2}{\left(x \right)}}{\left(x - 2\right)^{2}}\right) \sin{\left(x \right)} - 8 \log{\left(x - 2 \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{6 \sin^{2}{\left(x \right)}}{x - 2} + \frac{6 \cos^{2}{\left(x \right)}}{x - 2} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{\left(x - 2\right)^{2}} + \frac{2 \sin^{2}{\left(x \right)}}{\left(x - 2\right)^{3}}\right)$$