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- Derivative of:
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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^ three + four)^tan(x)
- (x cubed plus 4) to the power of tangent of (x)
- (x to the power of three plus four) to the power of tangent of (x)
- (x3+4)tan(x)
- x3+4tanx
- (x³+4)^tan(x)
- (x to the power of 3+4) to the power of tan(x)
- x^3+4^tanx
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Similar expressions
- (x^3-4)^tan(x)
Derivative of (x^3+4)^tan(x)
The solution
You have entered
[src]
tan(x) / 3 \ \x + 4/
$$\left(x^{3} + 4\right)^{\tan{\left(x \right)}}$$
(x^3 + 4)^tan(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]
tan(x) / 2 \
/ 3 \ |/ 2 \ / 3 \ 3*x *tan(x)|
\x + 4/ *|\1 + tan (x)/*log\x + 4/ + -----------|
| 3 |
\ x + 4 /
$$\left(x^{3} + 4\right)^{\tan{\left(x \right)}} \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)$$
The second derivative
[src]
/ 2 \
tan(x) |/ 2 \ 4 2 / 2 \|
/ 3\ ||/ 2 \ / 3\ 3*x *tan(x)| 9*x *tan(x) / 2 \ / 3\ 6*x*tan(x) 6*x *\1 + tan (x)/|
\4 + x / *||\1 + tan (x)/*log\4 + x / + -----------| - ----------- + 2*\1 + tan (x)/*log\4 + x /*tan(x) + ---------- + ------------------|
|| 3 | 2 3 3 |
|\ 4 + x / / 3\ 4 + x 4 + x |
\ \4 + x / /
$$\left(x^{3} + 4\right)^{\tan{\left(x \right)}} \left(- \frac{9 x^{4} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{6 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3} + 4} + \frac{6 x \tan{\left(x \right)}}{x^{3} + 4} + \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \tan{\left(x \right)}\right)$$
The third derivative
[src]
/ 3 \
tan(x) |/ 2 \ 2 / 2 \ / 4 2 / 2 \\ 3 4 / 2 \ / 2 \ 6 2 / 2 \ |
/ 3\ ||/ 2 \ / 3\ 3*x *tan(x)| / 2 \ / 3\ |/ 2 \ / 3\ 3*x *tan(x)| | 9*x *tan(x) / 2 \ / 3\ 6*x*tan(x) 6*x *\1 + tan (x)/| 6*tan(x) 54*x *tan(x) 27*x *\1 + tan (x)/ 2 / 2 \ / 3\ 18*x*\1 + tan (x)/ 54*x *tan(x) 18*x *\1 + tan (x)/*tan(x)|
\4 + x / *||\1 + tan (x)/*log\4 + x / + -----------| + 2*\1 + tan (x)/ *log\4 + x / + 3*|\1 + tan (x)/*log\4 + x / + -----------|*|- ----------- + 2*\1 + tan (x)/*log\4 + x /*tan(x) + ---------- + ------------------| + -------- - ------------ - ------------------- + 4*tan (x)*\1 + tan (x)/*log\4 + x / + ------------------ + ------------ + --------------------------|
|| 3 | | 3 | | 2 3 3 | 3 2 2 3 3 3 |
|\ 4 + x / \ 4 + x / | / 3\ 4 + x 4 + x | 4 + x / 3\ / 3\ 4 + x / 3\ 4 + x |
\ \ \4 + x / / \4 + x / \4 + x / \4 + x / /
$$\left(x^{3} + 4\right)^{\tan{\left(x \right)}} \left(\frac{54 x^{6} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{3}} - \frac{27 x^{4} \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{3} + 4\right)^{2}} - \frac{54 x^{3} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{18 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{3} + 4} + \frac{18 x \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3} + 4} + \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right)^{3} + 3 \left(\frac{3 x^{2} \tan{\left(x \right)}}{x^{3} + 4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)}\right) \left(- \frac{9 x^{4} \tan{\left(x \right)}}{\left(x^{3} + 4\right)^{2}} + \frac{6 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3} + 4} + \frac{6 x \tan{\left(x \right)}}{x^{3} + 4} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \tan{\left(x \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{3} + 4 \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{3} + 4 \right)} \tan^{2}{\left(x \right)} + \frac{6 \tan{\left(x \right)}}{x^{3} + 4}\right)$$
The graph