Mister Exam
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- 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 (-2)/x^3
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Derivative of e^(3/x)
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Derivative of (2*x+1)*(x^2+3*x-1)
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Derivative of (x*3)^(4-2*x)
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Identical expressions
- (x* three)^(four - two *x)
- (x multiply by 3) to the power of (4 minus 2 multiply by x)
- (x multiply by three) to the power of (four minus two multiply by x)
- (x*3)(4-2*x)
- x*34-2*x
- (x3)^(4-2x)
- (x3)(4-2x)
- x34-2x
- x3^4-2x
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Similar expressions
- (x*3)^(4+2*x)
Derivative of (x*3)^(4-2*x)
The solution
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]
4 - 2*x / 12 - 6*x\
(x*3) *|-2*log(x*3) + --------|
\ 3*x /
$$\left(3 x\right)^{4 - 2 x} \left(- 2 \log{\left(3 x \right)} + \frac{12 - 6 x}{3 x}\right)$$
The second derivative
[src]
/ -2 + x\
| 2 2 - ------|
4 - 2*x | /-2 + x \ x |
2*(3*x) *|2*|------ + log(3*x)| - ----------|
\ \ x / x /
$$2 \left(3 x\right)^{4 - 2 x} \left(2 \left(\log{\left(3 x \right)} + \frac{x - 2}{x}\right)^{2} - \frac{2 - \frac{x - 2}{x}}{x}\right)$$
The third derivative
[src]
/ 2*(-2 + x) / -2 + x\ /-2 + x \\
| 3 3 - ---------- 6*|2 - ------|*|------ + log(3*x)||
4 - 2*x | /-2 + x \ x \ x / \ x /|
2*(3*x) *|- 4*|------ + log(3*x)| + -------------- + ----------------------------------|
| \ x / 2 x |
\ x /
$$2 \left(3 x\right)^{4 - 2 x} \left(- 4 \left(\log{\left(3 x \right)} + \frac{x - 2}{x}\right)^{3} + \frac{6 \left(2 - \frac{x - 2}{x}\right) \left(\log{\left(3 x \right)} + \frac{x - 2}{x}\right)}{x} + \frac{3 - \frac{2 \left(x - 2\right)}{x}}{x^{2}}\right)$$
The graph