Mister Exam
Other calculators
- 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 1/3*x^3
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Derivative of x*x^(1/2)
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Derivative of x^(5/2)
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Derivative of (x-4)^2
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Identical expressions
- y=x^sinx+cosx
- y equally x to the power of sinus of x plus co sinus of e of x
- y=xsinx+cosx
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Similar expressions
- y=x^sinx-cosx
- y=x^(sinx+cosx)
Derivative of y=x^sinx+cosx
The solution
You have entered
[src]
sin(x) x + cos(x)
$$x^{\sin{\left(x \right)}} + \cos{\left(x \right)}$$
x^sin(x) + cos(x)
Detail solution
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Differentiate term by term:
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Don't know the steps in finding this derivative.
But the derivative is
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The derivative of cosine is negative sine:
The result is:
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The answer is:
The first derivative
[src]
sin(x) /sin(x) \
-sin(x) + x *|------ + cos(x)*log(x)|
\ x /
$$x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) - \sin{\left(x \right)}$$
The second derivative
[src]
2
sin(x) /sin(x) \ sin(x) /sin(x) 2*cos(x)\
-cos(x) + x *|------ + cos(x)*log(x)| - x *|------ + log(x)*sin(x) - --------|
\ x / | 2 x |
\ x /
$$x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} - x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - \cos{\left(x \right)}$$
The third derivative
[src]
3
sin(x) /sin(x) \ sin(x) / 2*sin(x) 3*sin(x) 3*cos(x)\ sin(x) /sin(x) \ /sin(x) 2*cos(x)\
x *|------ + cos(x)*log(x)| - x *|cos(x)*log(x) - -------- + -------- + --------| - 3*x *|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------| + sin(x)
\ x / | 3 x 2 | \ x / | 2 x |
\ x x / \ x /
$$x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} - 3 x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}\right) + \sin{\left(x \right)}$$
The graph