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Derivative of:
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Derivative of x^2+4*x+3
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

The derivative of the function/ y=(tg7x)^x^3

Derivative of y=(tg7x)^x^3

The solution

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          / 3\
          \x /
(tan(7*x))

\tan^{x^{3}}{\left(7 x \right)}

tan(7*x)^(x^3)

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

$\left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}$

The answer is:

\left(\log{\left(x^{3} \right)} + 1\right) \left(x^{3}\right)^{x^{3}}

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)}

Simplify

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)}

Simplify

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)}

Simplify

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Identical expressions

Derivative of y=(tg7x)^x^3

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