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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
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of 8
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Derivative of y=2x
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Derivative of sin(4x)
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Derivative of 11/x
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Identical expressions
- (x^ three + one)^(one /x)
- (x cubed plus 1) to the power of (1 divide by x)
- (x to the power of three plus one) to the power of (one divide by x)
- (x3+1)(1/x)
- x3+11/x
- (x³+1)^(1/x)
- (x to the power of 3+1) to the power of (1/x)
- x^3+1^1/x
- (x^3+1)^(1 divide by x)
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Similar expressions
- (x^3-1)^(1/x)
Derivative of (x^3+1)^(1/x)
The solution
You have entered
[src]
________ x / 3 \/ x + 1
$$\left(x^{3} + 1\right)^{\frac{1}{x}}$$
(x^3 + 1)^(1/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]
________ / / 3 \ \
x / 3 | log\x + 1/ 3*x |
\/ x + 1 *|- ----------- + ------|
| 2 3 |
\ x x + 1/
$$\left(x^{3} + 1\right)^{\frac{1}{x}} \left(\frac{3 x}{x^{3} + 1} - \frac{\log{\left(x^{3} + 1 \right)}}{x^{2}}\right)$$
The second derivative
[src]
/ 2 \
________ |/ / 3\ \ 3 / 3\|
x / 3 || log\1 + x / 3*x | 9*x 2*log\1 + x /|
\/ 1 + x *||- ----------- + ------| - --------- + -------------|
|| 2 3| 2 3 |
|\ x 1 + x / / 3\ x |
\ \1 + x / /
$$\left(x^{3} + 1\right)^{\frac{1}{x}} \left(- \frac{9 x^{3}}{\left(x^{3} + 1\right)^{2}} + \left(\frac{3 x}{x^{3} + 1} - \frac{\log{\left(x^{3} + 1 \right)}}{x^{2}}\right)^{2} + \frac{2 \log{\left(x^{3} + 1 \right)}}{x^{3}}\right)$$
The third derivative
[src]
/ 3 \
________ |/ / 3\ \ 2 / 3\ / / 3\ \ / / 3\ 3 \ 5 |
x / 3 || log\1 + x / 3*x | 27*x 6*log\1 + x / | log\1 + x / 3*x | | 2*log\1 + x / 9*x | 6 54*x |
\/ 1 + x *||- ----------- + ------| - --------- - ------------- - 3*|- ----------- + ------|*|- ------------- + ---------| + ---------- + ---------|
|| 2 3| 2 4 | 2 3| | 3 2| / 3\ 3|
|\ x 1 + x / / 3\ x \ x 1 + x / | x / 3\ | x*\1 + x / / 3\ |
\ \1 + x / \ \1 + x / / \1 + x / /
$$\left(x^{3} + 1\right)^{\frac{1}{x}} \left(\frac{54 x^{5}}{\left(x^{3} + 1\right)^{3}} - \frac{27 x^{2}}{\left(x^{3} + 1\right)^{2}} + \left(\frac{3 x}{x^{3} + 1} - \frac{\log{\left(x^{3} + 1 \right)}}{x^{2}}\right)^{3} - 3 \left(\frac{3 x}{x^{3} + 1} - \frac{\log{\left(x^{3} + 1 \right)}}{x^{2}}\right) \left(\frac{9 x^{3}}{\left(x^{3} + 1\right)^{2}} - \frac{2 \log{\left(x^{3} + 1 \right)}}{x^{3}}\right) + \frac{6}{x \left(x^{3} + 1\right)} - \frac{6 \log{\left(x^{3} + 1 \right)}}{x^{4}}\right)$$