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How to use it?
- Derivative of:
- Derivative of x^e^x
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Derivative of x+lnx
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Derivative of (x^4-x-1)^4
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Derivative of (x^4+5)^cot(x)
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Identical expressions
- (x^ four + five)^cot(x)
- (x to the power of 4 plus 5) to the power of cotangent of (x)
- (x to the power of four plus five) to the power of cotangent of (x)
- (x4+5)cot(x)
- x4+5cotx
- (x⁴+5)^cot(x)
- x^4+5^cotx
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Similar expressions
- (x^4-5)^cot(x)
Derivative of (x^4+5)^cot(x)
The solution
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[src]
cot(x) / 4 \ \x + 5/
$$\left(x^{4} + 5\right)^{\cot{\left(x \right)}}$$
(x^4 + 5)^cot(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]
cot(x) / 3 \
/ 4 \ |/ 2 \ / 4 \ 4*x *cot(x)|
\x + 5/ *|\-1 - cot (x)/*log\x + 5/ + -----------|
| 4 |
\ x + 5 /
$$\left(x^{4} + 5\right)^{\cot{\left(x \right)}} \left(\frac{4 x^{3} \cot{\left(x \right)}}{x^{4} + 5} + \left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(x^{4} + 5 \right)}\right)$$
The second derivative
[src]
/ 2 \
cot(x) |/ 3 \ 6 3 / 2 \ 2 |
/ 4\ || / 2 \ / 4\ 4*x *cot(x)| 16*x *cot(x) 8*x *\1 + cot (x)/ / 2 \ / 4\ 12*x *cot(x)|
\5 + x / *||- \1 + cot (x)/*log\5 + x / + -----------| - ------------ - ------------------ + 2*\1 + cot (x)/*cot(x)*log\5 + x / + ------------|
|| 4 | 2 4 4 |
|\ 5 + x / / 4\ 5 + x 5 + x |
\ \5 + x / /
$$\left(x^{4} + 5\right)^{\cot{\left(x \right)}} \left(- \frac{16 x^{6} \cot{\left(x \right)}}{\left(x^{4} + 5\right)^{2}} - \frac{8 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{4} + 5} + \frac{12 x^{2} \cot{\left(x \right)}}{x^{4} + 5} + \left(\frac{4 x^{3} \cot{\left(x \right)}}{x^{4} + 5} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 5 \right)}\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 5 \right)} \cot{\left(x \right)}\right)$$
The third derivative
[src]
/ 3 \
cot(x) |/ 3 \ / 3 \ / 2 3 / 2 \ 6 \ 2 5 2 / 2 \ 6 / 2 \ 9 3 / 2 \ |
/ 4\ || / 2 \ / 4\ 4*x *cot(x)| | / 2 \ / 4\ 4*x *cot(x)| | / 2 \ / 4\ 6*x *cot(x) 4*x *\1 + cot (x)/ 8*x *cot(x)| / 2 \ / 4\ 144*x *cot(x) 36*x *\1 + cot (x)/ 2 / 2 \ / 4\ 24*x*cot(x) 48*x *\1 + cot (x)/ 128*x *cot(x) 24*x *\1 + cot (x)/*cot(x)|
\5 + x / *||- \1 + cot (x)/*log\5 + x / + -----------| - 6*|- \1 + cot (x)/*log\5 + x / + -----------|*|- \1 + cot (x)/*cot(x)*log\5 + x / - ----------- + ------------------ + -----------| - 2*\1 + cot (x)/ *log\5 + x / - ------------- - ------------------- - 4*cot (x)*\1 + cot (x)/*log\5 + x / + ----------- + ------------------- + ------------- + --------------------------|
|| 4 | | 4 | | 4 4 2 | 2 4 4 2 3 4 |
|\ 5 + x / \ 5 + x / | 5 + x 5 + x / 4\ | / 4\ 5 + x 5 + x / 4\ / 4\ 5 + x |
\ \ \5 + x / / \5 + x / \5 + x / \5 + x / /
$$\left(x^{4} + 5\right)^{\cot{\left(x \right)}} \left(\frac{128 x^{9} \cot{\left(x \right)}}{\left(x^{4} + 5\right)^{3}} + \frac{48 x^{6} \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(x^{4} + 5\right)^{2}} - \frac{144 x^{5} \cot{\left(x \right)}}{\left(x^{4} + 5\right)^{2}} + \frac{24 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x^{4} + 5} - \frac{36 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{4} + 5} + \frac{24 x \cot{\left(x \right)}}{x^{4} + 5} + \left(\frac{4 x^{3} \cot{\left(x \right)}}{x^{4} + 5} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 5 \right)}\right)^{3} - 6 \left(\frac{4 x^{3} \cot{\left(x \right)}}{x^{4} + 5} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 5 \right)}\right) \left(\frac{8 x^{6} \cot{\left(x \right)}}{\left(x^{4} + 5\right)^{2}} + \frac{4 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{4} + 5} - \frac{6 x^{2} \cot{\left(x \right)}}{x^{4} + 5} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 5 \right)} \cot{\left(x \right)}\right) - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{4} + 5 \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{4} + 5 \right)} \cot^{2}{\left(x \right)}\right)$$
The graph