Mister Exam
Other calculators
- 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
-
How to use it?
- Derivative of:
-
Derivative of 3*x^5-2*x^2
-
Derivative of 2^x*sin(x)
-
Derivative of (1/x)^x
-
Derivative of x-ln(1+x)
-
Identical expressions
- (x+ two ^(one / two))^(exp(one /(x- four)))
- (x plus 2 to the power of (1 divide by 2)) to the power of ( exponent of (1 divide by (x minus 4)))
- (x plus two to the power of (one divide by two)) to the power of ( exponent of (one divide by (x minus four)))
- (x+2(1/2))(exp(1/(x-4)))
- x+21/2exp1/x-4
- x+2^1/2^exp1/x-4
- (x+2^(1 divide by 2))^(exp(1 divide by (x-4)))
-
Similar expressions
- (x+2^(1/2))^(exp(1/(x+4)))
- (x-2^(1/2))^(exp(1/(x-4)))
Derivative of (x+2^(1/2))^(exp(1/(x-4)))
The solution
You have entered
[src]
/ 1 \
| -----|
| x - 4|
\e /
/ ___\
\x + \/ 2 /
$$\left(x + \sqrt{2}\right)^{e^{\frac{1}{x - 4}}}$$
(x + sqrt(2))^exp(1/(x - 4))
Detail solution
-
Don't know the steps in finding this derivative.
But the derivative is
-
Now simplify:
The answer is:
The first derivative
[src]
/ 1 \
| -----| / 1 1 \
| x - 4| | ----- ----- |
\e / | x - 4 x - 4 / ___\|
/ ___\ | e e *log\x + \/ 2 /|
\x + \/ 2 / *|--------- - ---------------------|
| ___ 2 |
\x + \/ 2 (x - 4) /
$$\left(x + \sqrt{2}\right)^{e^{\frac{1}{x - 4}}} \left(\frac{e^{\frac{1}{x - 4}}}{x + \sqrt{2}} - \frac{e^{\frac{1}{x - 4}} \log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{2}}\right)$$
The second derivative
[src]
/ 1 \
| ------|
| -4 + x| / 2 1 \ 1
\e / | / ___\ / / ___\\ ------ / ___\| ------
/ ___\ | 1 log\x + \/ 2 / | 1 log\x + \/ 2 /| -4 + x 2 2*log\x + \/ 2 /| -4 + x
\x + \/ 2 / *|- ------------ + -------------- + |--------- - --------------| *e - --------------------- + ----------------|*e
| 2 4 | ___ 2 | 2 / ___\ 3 |
| / ___\ (-4 + x) \x + \/ 2 (-4 + x) / (-4 + x) *\x + \/ 2 / (-4 + x) |
\ \x + \/ 2 / /
$$\left(x + \sqrt{2}\right)^{e^{\frac{1}{x - 4}}} \left(\left(\frac{1}{x + \sqrt{2}} - \frac{\log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{2}}\right)^{2} e^{\frac{1}{x - 4}} - \frac{1}{\left(x + \sqrt{2}\right)^{2}} - \frac{2}{\left(x - 4\right)^{2} \left(x + \sqrt{2}\right)} + \frac{2 \log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{3}} + \frac{\log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{4}}\right) e^{\frac{1}{x - 4}}$$
The third derivative
[src]
/ 1 \
| ------|
| -4 + x| / 3 2 1 \ 1
\e / | / / ___\\ ------ / ___\ / ___\ / ___\ / / ___\\ / / ___\ / ___\ \ ------| ------
/ ___\ | 2 | 1 log\x + \/ 2 /| -4 + x log\x + \/ 2 / 6*log\x + \/ 2 / 6*log\x + \/ 2 / 3 3 6 | 1 log\x + \/ 2 /| | 1 log\x + \/ 2 / 2*log\x + \/ 2 / 2 | -4 + x| -4 + x
\x + \/ 2 / *|------------ + |--------- - --------------| *e - -------------- - ---------------- - ---------------- + --------------------- + ---------------------- + --------------------- - 3*|--------- - --------------|*|------------ - -------------- - ---------------- + ---------------------|*e |*e
| 3 | ___ 2 | 6 5 4 4 / ___\ 2 3 / ___\ | ___ 2 | | 2 4 3 2 / ___\| |
|/ ___\ \x + \/ 2 (-4 + x) / (-4 + x) (-4 + x) (-4 + x) (-4 + x) *\x + \/ 2 / 2 / ___\ (-4 + x) *\x + \/ 2 / \x + \/ 2 (-4 + x) / |/ ___\ (-4 + x) (-4 + x) (-4 + x) *\x + \/ 2 /| |
\\x + \/ 2 / (-4 + x) *\x + \/ 2 / \\x + \/ 2 / / /
$$\left(x + \sqrt{2}\right)^{e^{\frac{1}{x - 4}}} \left(\left(\frac{1}{x + \sqrt{2}} - \frac{\log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{2}}\right)^{3} e^{\frac{2}{x - 4}} - 3 \left(\frac{1}{x + \sqrt{2}} - \frac{\log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{2}}\right) \left(\frac{1}{\left(x + \sqrt{2}\right)^{2}} + \frac{2}{\left(x - 4\right)^{2} \left(x + \sqrt{2}\right)} - \frac{2 \log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{3}} - \frac{\log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{4}}\right) e^{\frac{1}{x - 4}} + \frac{2}{\left(x + \sqrt{2}\right)^{3}} + \frac{3}{\left(x - 4\right)^{2} \left(x + \sqrt{2}\right)^{2}} + \frac{6}{\left(x - 4\right)^{3} \left(x + \sqrt{2}\right)} - \frac{6 \log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{4}} + \frac{3}{\left(x - 4\right)^{4} \left(x + \sqrt{2}\right)} - \frac{6 \log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{5}} - \frac{\log{\left(x + \sqrt{2} \right)}}{\left(x - 4\right)^{6}}\right) e^{\frac{1}{x - 4}}$$