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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of e^(-x)
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Derivative of tg2x
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Derivative of (x/3)
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Derivative of (x^2-3x)^x
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Identical expressions
- (x^ two -3x)^x
- (x squared minus 3x) to the power of x
- (x to the power of two minus 3x) to the power of x
- (x2-3x)x
- x2-3xx
- (x²-3x)^x
- (x to the power of 2-3x) to the power of x
- x^2-3x^x
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Similar expressions
- (x^2+3x)^x
Derivative of (x^2-3x)^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]
x
/ 2 \ /x*(-3 + 2*x) / 2 \\
\x - 3*x/ *|------------ + log\x - 3*x/|
| 2 |
\ x - 3*x /
$$\left(x^{2} - 3 x\right)^{x} \left(\frac{x \left(2 x - 3\right)}{x^{2} - 3 x} + \log{\left(x^{2} - 3 x \right)}\right)$$
The second derivative
[src]
/ 2\
| 2*(-3 + 2*x) (-3 + 2*x) |
| 2 2 + ------------ - -----------|
x |/-3 + 2*x \ x x*(-3 + x)|
(x*(-3 + x)) *||-------- + log(x*(-3 + x))| + ------------------------------|
\\ -3 + x / -3 + x /
$$\left(x \left(x - 3\right)\right)^{x} \left(\left(\log{\left(x \left(x - 3\right) \right)} + \frac{2 x - 3}{x - 3}\right)^{2} + \frac{2 + \frac{2 \left(2 x - 3\right)}{x} - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}}{x - 3}\right)$$
The third derivative
[src]
/ 2 3 \
| 6*(-3 + 2*x) 3*(-3 + 2*x) 2*(-3 + 2*x) / 2\|
| 6 - ------------ - ------------- + ------------- /-3 + 2*x \ | 2*(-3 + 2*x) (-3 + 2*x) ||
| 3 -3 + x x*(-3 + x) 2 3*|-------- + log(x*(-3 + x))|*|2 + ------------ - -----------||
x |/-3 + 2*x \ x*(-3 + x) \ -3 + x / \ x x*(-3 + x)/|
(x*(-3 + x)) *||-------- + log(x*(-3 + x))| + ------------------------------------------------ + ---------------------------------------------------------------|
\\ -3 + x / x*(-3 + x) -3 + x /
$$\left(x \left(x - 3\right)\right)^{x} \left(\left(\log{\left(x \left(x - 3\right) \right)} + \frac{2 x - 3}{x - 3}\right)^{3} + \frac{3 \left(\log{\left(x \left(x - 3\right) \right)} + \frac{2 x - 3}{x - 3}\right) \left(2 + \frac{2 \left(2 x - 3\right)}{x} - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right)}{x - 3} + \frac{6 - \frac{6 \left(2 x - 3\right)}{x - 3} - \frac{3 \left(2 x - 3\right)^{2}}{x \left(x - 3\right)} + \frac{2 \left(2 x - 3\right)^{3}}{x \left(x - 3\right)^{2}}}{x \left(x - 3\right)}\right)$$
The graph