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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of (1+sqrt(x))/(1-sqrt(x))
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Derivative of y=5-4x+7x³-x^5
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Derivative of x/(x^2+4)
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Derivative of y=3cos(5x+6)
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Identical expressions
- two *x^sin(x)
- 2 multiply by x to the power of sinus of (x)
- two multiply by x to the power of sinus of (x)
- 2*xsin(x)
- 2*xsinx
- 2x^sin(x)
- 2xsin(x)
- 2xsinx
- 2x^sinx
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Similar expressions
- 2*x^sinx
Derivative of 2*x^sin(x)
The solution
You have entered
[src]
sin(x) 2*x
$$2 x^{\sin{\left(x \right)}}$$
d / sin(x)\ --\2*x / dx
$$\frac{d}{d x} 2 x^{\sin{\left(x \right)}}$$
Detail solution
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The derivative of a constant times a function is the constant times the derivative of the function.
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Don't know the steps in finding this derivative.
But the derivative is
So, the result is:
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The answer is:
The first derivative
[src]
sin(x) /sin(x) \
2*x *|------ + cos(x)*log(x)|
\ x /
$$2 x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)$$
The second derivative
[src]
/ 2 \
sin(x) |/sin(x) \ sin(x) 2*cos(x)|
2*x *||------ + cos(x)*log(x)| - ------ - log(x)*sin(x) + --------|
|\ x / 2 x |
\ x /
$$2 x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 \
sin(x) | /sin(x) \ 2*sin(x) 3*sin(x) 3*cos(x) /sin(x) \ /sin(x) 2*cos(x)\|
-2*x *|- |------ + cos(x)*log(x)| + cos(x)*log(x) - -------- + -------- + -------- + 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------||
| \ x / 3 x 2 \ x / | 2 x ||
\ x x \ x //
$$- 2 x^{\sin{\left(x \right)}} \left(- \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) + \log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}\right)$$
The graph