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- Derivative of a implicit defined function
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- Partial derivative of the function
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of y=√4-x^2
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Derivative of x^2/(x+2)
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Derivative of x^2*tgx
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Derivative of sin3x^2
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Identical expressions
- (x+ four)^sin(five *x)
- (x plus 4) to the power of sinus of (5 multiply by x)
- (x plus four) to the power of sinus of (five multiply by x)
- (x+4)sin(5*x)
- x+4sin5*x
- (x+4)^sin(5x)
- (x+4)sin(5x)
- x+4sin5x
- x+4^sin5x
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Similar expressions
- (x-4)^sin(5*x)
Derivative of (x+4)^sin(5*x)
The solution
You have entered
[src]
sin(5*x) (x + 4)
$$\left(x + 4\right)^{\sin{\left(5 x \right)}}$$
(x + 4)^sin(5*x)
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]
sin(5*x) /sin(5*x) \
(x + 4) *|-------- + 5*cos(5*x)*log(x + 4)|
\ x + 4 /
$$\left(x + 4\right)^{\sin{\left(5 x \right)}} \left(5 \log{\left(x + 4 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 4}\right)$$
The second derivative
[src]
/ 2 \
sin(5*x) |/sin(5*x) \ sin(5*x) 10*cos(5*x)|
(4 + x) *||-------- + 5*cos(5*x)*log(4 + x)| - -------- - 25*log(4 + x)*sin(5*x) + -----------|
|\ 4 + x / 2 4 + x |
\ (4 + x) /
$$\left(x + 4\right)^{\sin{\left(5 x \right)}} \left(\left(5 \log{\left(x + 4 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 4}\right)^{2} - 25 \log{\left(x + 4 \right)} \sin{\left(5 x \right)} + \frac{10 \cos{\left(5 x \right)}}{x + 4} - \frac{\sin{\left(5 x \right)}}{\left(x + 4\right)^{2}}\right)$$
The third derivative
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/ 3 \
sin(5*x) |/sin(5*x) \ 75*sin(5*x) 15*cos(5*x) /sin(5*x) \ /sin(5*x) 10*cos(5*x) \ 2*sin(5*x)|
(4 + x) *||-------- + 5*cos(5*x)*log(4 + x)| - 125*cos(5*x)*log(4 + x) - ----------- - ----------- - 3*|-------- + 5*cos(5*x)*log(4 + x)|*|-------- - ----------- + 25*log(4 + x)*sin(5*x)| + ----------|
|\ 4 + x / 4 + x 2 \ 4 + x / | 2 4 + x | 3 |
\ (4 + x) \(4 + x) / (4 + x) /
$$\left(x + 4\right)^{\sin{\left(5 x \right)}} \left(\left(5 \log{\left(x + 4 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 4}\right)^{3} - 3 \left(5 \log{\left(x + 4 \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x + 4}\right) \left(25 \log{\left(x + 4 \right)} \sin{\left(5 x \right)} - \frac{10 \cos{\left(5 x \right)}}{x + 4} + \frac{\sin{\left(5 x \right)}}{\left(x + 4\right)^{2}}\right) - 125 \log{\left(x + 4 \right)} \cos{\left(5 x \right)} - \frac{75 \sin{\left(5 x \right)}}{x + 4} - \frac{15 \cos{\left(5 x \right)}}{\left(x + 4\right)^{2}} + \frac{2 \sin{\left(5 x \right)}}{\left(x + 4\right)^{3}}\right)$$