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- Derivative of:
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Derivative of (4x-3)^2
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Derivative of y=√4-x^2
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Derivative of x^(x^2+1)
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Derivative of (x-3)/sqrt(x)
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Identical expressions
- (с*x+c)^e^(-2x)
- (с multiply by x plus c) to the power of e to the power of ( minus 2x)
- (с*x+c)e(-2x)
- с*x+ce-2x
- (сx+c)^e^(-2x)
- (сx+c)e(-2x)
- сx+ce-2x
- сx+c^e^-2x
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Similar expressions
- (с*x+c)^e^(2x)
- (с*x-c)^e^(-2x)
Derivative of (с*x+c)^e^(-2x)
The solution
You have entered
[src]
/ -2*x\
\e /
(c*x + c)
$$\left(c x + c\right)^{e^{- 2 x}}$$
/ / -2*x\\ d | \e /| --\(c*x + c) / dx
$$\frac{\partial}{\partial x} \left(c x + c\right)^{e^{- 2 x}}$$
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]
/ -2*x\ / -2*x\
\e / | -2*x c*e |
(c*x + c) *|- 2*e *log(c*x + c) + -------|
\ c*x + c/
$$\left(c x + c\right)^{e^{- 2 x}} \left(\frac{c e^{- 2 x}}{c x + c} - 2 e^{- 2 x} \log{\left(c x + c \right)}\right)$$
The second derivative
[src]
/ -2*x\ / 2 \
\e / | 1 4 / 1 \ -2*x| -2*x
(c*(1 + x)) *|- -------- - ----- + 4*log(c*(1 + x)) + |----- - 2*log(c*(1 + x))| *e |*e
| 2 1 + x \1 + x / |
\ (1 + x) /
$$\left(c \left(x + 1\right)\right)^{e^{- 2 x}} \left(\left(- 2 \log{\left(c \left(x + 1\right) \right)} + \frac{1}{x + 1}\right)^{2} e^{- 2 x} + 4 \log{\left(c \left(x + 1\right) \right)} - \frac{4}{x + 1} - \frac{1}{\left(x + 1\right)^{2}}\right) e^{- 2 x}$$
The third derivative
[src]
/ -2*x\ / 3 \
\e / | 2 6 12 / 1 \ -4*x / 1 \ / 1 4 \ -2*x| -2*x
(c*(1 + x)) *|-8*log(c*(1 + x)) + -------- + -------- + ----- + |----- - 2*log(c*(1 + x))| *e - 3*|----- - 2*log(c*(1 + x))|*|-------- - 4*log(c*(1 + x)) + -----|*e |*e
| 3 2 1 + x \1 + x / \1 + x / | 2 1 + x| |
\ (1 + x) (1 + x) \(1 + x) / /
$$\left(c \left(x + 1\right)\right)^{e^{- 2 x}} \left(\left(- 2 \log{\left(c \left(x + 1\right) \right)} + \frac{1}{x + 1}\right)^{3} e^{- 4 x} - 3 \left(- 2 \log{\left(c \left(x + 1\right) \right)} + \frac{1}{x + 1}\right) \left(- 4 \log{\left(c \left(x + 1\right) \right)} + \frac{4}{x + 1} + \frac{1}{\left(x + 1\right)^{2}}\right) e^{- 2 x} - 8 \log{\left(c \left(x + 1\right) \right)} + \frac{12}{x + 1} + \frac{6}{\left(x + 1\right)^{2}} + \frac{2}{\left(x + 1\right)^{3}}\right) e^{- 2 x}$$