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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 1/x^8
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Derivative of (x^2)/36
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Derivative of x^2*e^(3-2*x)*log(2)^x
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Derivative of (x-1)/(x^2+1)
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Identical expressions
- y=(tg7x)^x^ three
- y equally (tg7x) to the power of x cubed
- y equally (tg7x) to the power of x to the power of three
- y=(tg7x)x3
- y=tg7xx3
- y=(tg7x)^x³
- y=(tg7x) to the power of x to the power of 3
- y=tg7x^x^3
Derivative of y=(tg7x)^x^3
The solution
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\ / 3 / 2 \\
\x / | 2 x *\7 + 7*tan (7*x)/|
(tan(7*x)) *|3*x *log(tan(7*x)) + --------------------|
\ tan(7*x) /
$$\left(\frac{x^{3} \left(7 \tan^{2}{\left(7 x \right)} + 7\right)}{\tan{\left(7 x \right)}} + 3 x^{2} \log{\left(\tan{\left(7 x \right)} \right)}\right) \tan^{x^{3}}{\left(7 x \right)}$$
The second derivative
[src]
/ 2 2 \
/ 3\ | / / 2 \\ 2 / 2 \ / 2 \|
\x / | 3 | 7*x*\1 + tan (7*x)/| 2 / 2 \ 49*x *\1 + tan (7*x)/ 42*x*\1 + tan (7*x)/|
x*(tan(7*x)) *|6*log(tan(7*x)) + x *|3*log(tan(7*x)) + -------------------| + 98*x *\1 + tan (7*x)/ - ---------------------- + --------------------|
| \ tan(7*x) / 2 tan(7*x) |
\ tan (7*x) /
$$x \left(x^{3} \left(\frac{7 x \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + 3 \log{\left(\tan{\left(7 x \right)} \right)}\right)^{2} - \frac{49 x^{2} \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2}}{\tan^{2}{\left(7 x \right)}} + 98 x^{2} \left(\tan^{2}{\left(7 x \right)} + 1\right) + \frac{42 x \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + 6 \log{\left(\tan{\left(7 x \right)} \right)}\right) \tan^{x^{3}}{\left(7 x \right)}$$
The third derivative
[src]
/ 3 2 2 / 2 \ 3 \
/ 3\ | / / 2 \\ 3 / 2 \ 2 / 2 \ / / 2 \\ | 2 / 2 \ / 2 \| / 2 \ 3 / 2 \ |
\x / | 6 | 7*x*\1 + tan (7*x)/| 2 / 2 \ 1372*x *\1 + tan (7*x)/ 441*x *\1 + tan (7*x)/ 3 | 7*x*\1 + tan (7*x)/| | 2 / 2 \ 49*x *\1 + tan (7*x)/ 42*x*\1 + tan (7*x)/| 126*x*\1 + tan (7*x)/ 686*x *\1 + tan (7*x)/ 3 / 2 \ |
(tan(7*x)) *|6*log(tan(7*x)) + x *|3*log(tan(7*x)) + -------------------| + 882*x *\1 + tan (7*x)/ - ------------------------ - ----------------------- + 3*x *|3*log(tan(7*x)) + -------------------|*|6*log(tan(7*x)) + 98*x *\1 + tan (7*x)/ - ---------------------- + --------------------| + --------------------- + ----------------------- + 1372*x *\1 + tan (7*x)/*tan(7*x)|
| \ tan(7*x) / tan(7*x) 2 \ tan(7*x) / | 2 tan(7*x) | tan(7*x) 3 |
\ tan (7*x) \ tan (7*x) / tan (7*x) /
$$\left(x^{6} \left(\frac{7 x \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + 3 \log{\left(\tan{\left(7 x \right)} \right)}\right)^{3} + 3 x^{3} \left(\frac{7 x \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + 3 \log{\left(\tan{\left(7 x \right)} \right)}\right) \left(- \frac{49 x^{2} \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2}}{\tan^{2}{\left(7 x \right)}} + 98 x^{2} \left(\tan^{2}{\left(7 x \right)} + 1\right) + \frac{42 x \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + 6 \log{\left(\tan{\left(7 x \right)} \right)}\right) + \frac{686 x^{3} \left(\tan^{2}{\left(7 x \right)} + 1\right)^{3}}{\tan^{3}{\left(7 x \right)}} - \frac{1372 x^{3} \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2}}{\tan{\left(7 x \right)}} + 1372 x^{3} \left(\tan^{2}{\left(7 x \right)} + 1\right) \tan{\left(7 x \right)} - \frac{441 x^{2} \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2}}{\tan^{2}{\left(7 x \right)}} + 882 x^{2} \left(\tan^{2}{\left(7 x \right)} + 1\right) + \frac{126 x \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + 6 \log{\left(\tan{\left(7 x \right)} \right)}\right) \tan^{x^{3}}{\left(7 x \right)}$$