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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 5-7x
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of f(x)=5
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Derivative of 3^(1/x)
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Identical expressions
- x^(sin(x^ three))
- x to the power of ( sinus of (x cubed ))
- x to the power of ( sinus of (x to the power of three))
- x(sin(x3))
- xsinx3
- x^(sin(x³))
- x to the power of (sin(x to the power of 3))
- x^sinx^3
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Similar expressions
- y=x^sinx^3
Derivative of x^(sin(x^3))
The solution
You have entered
[src]
/ 3\ sin\x / x
$$x^{\sin{\left(x^{3} \right)}}$$
/ / 3\\ d | sin\x /| --\x / dx
$$\frac{d}{d x} x^{\sin{\left(x^{3} \right)}}$$
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
[src]
/ 3\ / / 3\ \
sin\x / |sin\x / 2 / 3\ |
x *|------- + 3*x *cos\x /*log(x)|
\ x /
$$x^{\sin{\left(x^{3} \right)}} \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right)$$
The second derivative
[src]
/ 2 \
/ 3\ |/ / 3\ \ / 3\ |
sin\x / ||sin\x / 2 / 3\ | sin\x / / 3\ 4 / 3\ / 3\ |
x *||------- + 3*x *cos\x /*log(x)| - ------- + 6*x*cos\x / - 9*x *log(x)*sin\x / + 6*x*cos\x /*log(x)|
|\ x / 2 |
\ x /
$$x^{\sin{\left(x^{3} \right)}} \left(- 9 x^{4} \log{\left(x \right)} \sin{\left(x^{3} \right)} + 6 x \log{\left(x \right)} \cos{\left(x^{3} \right)} + 6 x \cos{\left(x^{3} \right)} + \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right)^{2} - \frac{\sin{\left(x^{3} \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 \
/ 3\ |/ / 3\ \ / / 3\ \ / / 3\ \ / 3\ |
sin\x / ||sin\x / 2 / 3\ | / 3\ 3 / 3\ |sin\x / 2 / 3\ | |sin\x / / 3\ / 3\ 4 / 3\| 2*sin\x / / 3\ 3 / 3\ 6 / 3\ |
x *||------- + 3*x *cos\x /*log(x)| + 9*cos\x / - 27*x *sin\x / - 3*|------- + 3*x *cos\x /*log(x)|*|------- - 6*x*cos\x / - 6*x*cos\x /*log(x) + 9*x *log(x)*sin\x /| + --------- + 6*cos\x /*log(x) - 54*x *log(x)*sin\x / - 27*x *cos\x /*log(x)|
|\ x / \ x / | 2 | 3 |
\ \ x / x /
$$x^{\sin{\left(x^{3} \right)}} \left(- 27 x^{6} \log{\left(x \right)} \cos{\left(x^{3} \right)} - 54 x^{3} \log{\left(x \right)} \sin{\left(x^{3} \right)} - 27 x^{3} \sin{\left(x^{3} \right)} + \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right)^{3} - 3 \cdot \left(3 x^{2} \log{\left(x \right)} \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x}\right) \left(9 x^{4} \log{\left(x \right)} \sin{\left(x^{3} \right)} - 6 x \log{\left(x \right)} \cos{\left(x^{3} \right)} - 6 x \cos{\left(x^{3} \right)} + \frac{\sin{\left(x^{3} \right)}}{x^{2}}\right) + 6 \log{\left(x \right)} \cos{\left(x^{3} \right)} + 9 \cos{\left(x^{3} \right)} + \frac{2 \sin{\left(x^{3} \right)}}{x^{3}}\right)$$
The graph