Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of x^3/(x+1)^2
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Derivative of 3-5*x
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Derivative of 2*y^2
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Derivative of 2*x^3-3*x^2+6*x+1
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Identical expressions
- y=(sqrt(five -x))^x^ two
- y equally ( square root of (5 minus x)) to the power of x squared
- y equally ( square root of (five minus x)) to the power of x to the power of two
- y=(√(5-x))^x^2
- y=(sqrt(5-x))x2
- y=sqrt5-xx2
- y=(sqrt(5-x))^x²
- y=(sqrt(5-x)) to the power of x to the power of 2
- y=sqrt5-x^x^2
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Similar expressions
- y=(sqrt(5+x))^x^2
Derivative of y=(sqrt(5-x))^x^2
The solution
You have entered
[src]
/ 2\
\x /
_______
\/ 5 - x
$$\left(\sqrt{5 - x}\right)^{x^{2}}$$
/ / 2\\ | \x /| d | _______ | --\\/ 5 - x / dx
$$\frac{d}{d x} \left(\sqrt{5 - x}\right)^{x^{2}}$$
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 \
2 | / _______\ x |
(5 - x) *|2*x*log\\/ 5 - x / - ---------|
\ 2*(5 - x)/
$$\left(5 - x\right)^{\frac{x^{2}}{2}} \left(- \frac{x^{2}}{2 \cdot \left(5 - x\right)} + 2 x \log{\left(\sqrt{5 - x} \right)}\right)$$
The second derivative
[src]
2
x / 2 / x \ / / _______\ x \\
-- | 2 x *|2*log(5 - x) + ------|*|4*log\\/ 5 - x / + ------||
2 | / _______\ 2*x x \ -5 + x/ \ -5 + x/|
(5 - x) *|2*log\\/ 5 - x / + ------ - ----------- + ------------------------------------------------------|
| -5 + x 2 4 |
\ 2*(-5 + x) /
$$\left(5 - x\right)^{\frac{x^{2}}{2}} \left(\frac{x^{2} \left(\frac{x}{x - 5} + 4 \log{\left(\sqrt{5 - x} \right)}\right) \left(\frac{x}{x - 5} + 2 \log{\left(5 - x \right)}\right)}{4} - \frac{x^{2}}{2 \left(x - 5\right)^{2}} + \frac{2 x}{x - 5} + 2 \log{\left(\sqrt{5 - x} \right)}\right)$$
The third derivative
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/ 2 / 2 \ / 2 \ \
2 | x 3*x / x \ | / _______\ x 4*x | / / _______\ x \ | x 4*x | 2 |
x |3 + --------- - ------ x*|2*log(5 - x) + ------|*|4*log\\/ 5 - x / - --------- + ------| x*|4*log\\/ 5 - x / + ------|*|2*log(5 - x) - --------- + ------| 3 / x \ / / _______\ x \|
-- | 2 -5 + x \ -5 + x/ | 2 -5 + x| \ -5 + x/ | 2 -5 + x| x *|2*log(5 - x) + ------| *|4*log\\/ 5 - x / + ------||
2 | (-5 + x) \ (-5 + x) / \ (-5 + x) / \ -5 + x/ \ -5 + x/|
(5 - x) *|---------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- + -------------------------------------------------------|
\ -5 + x 2 4 8 /
$$\left(5 - x\right)^{\frac{x^{2}}{2}} \left(\frac{x^{3} \left(\frac{x}{x - 5} + 4 \log{\left(\sqrt{5 - x} \right)}\right) \left(\frac{x}{x - 5} + 2 \log{\left(5 - x \right)}\right)^{2}}{8} + \frac{x \left(\frac{x}{x - 5} + 4 \log{\left(\sqrt{5 - x} \right)}\right) \left(- \frac{x^{2}}{\left(x - 5\right)^{2}} + \frac{4 x}{x - 5} + 2 \log{\left(5 - x \right)}\right)}{4} + \frac{x \left(\frac{x}{x - 5} + 2 \log{\left(5 - x \right)}\right) \left(- \frac{x^{2}}{\left(x - 5\right)^{2}} + \frac{4 x}{x - 5} + 4 \log{\left(\sqrt{5 - x} \right)}\right)}{2} + \frac{\frac{x^{2}}{\left(x - 5\right)^{2}} - \frac{3 x}{x - 5} + 3}{x - 5}\right)$$
The graph