Find the derivative of $x^{-4}(3-4x^{-5})$.

If $f^{\prime}(x)=k(\cos x-\sin x)$,$f^{\prime}(0)=3$,and $f\left(\frac{\pi}{2}\right)=15$,then $f(x)=$

The differential coefficient of ${\left( {{x^{\frac{{\ell + m}}{{m - n}}}}} \right)^{\frac{1}{{n - \ell }}}} \cdot {\left( {{x^{\frac{{m + n}}{{n - \ell }}}}} \right)^{\frac{1}{{\ell - m}}}} \cdot {\left( {{x^{\frac{{n + \ell }}{{\ell - m}}}}} \right)^{\frac{1}{{m - n}}}}$ with respect to $x$ is:

Let $g(x) \neq 0, g^{\prime}(x) \neq 0, f(x) \neq 0, f^{\prime}(x) \neq 0$. If $F(x)=f(x) g(x)$,$G(x)=f^{\prime}(x) g^{\prime}(x)$,$F^{\prime}(x)=G(x) H(x)$,and $F^{\prime}(x)=F(x) K(x)$,then $H(x)+K(x)=$

If $x \neq 0$ and $f(x)$ satisfies $8 f(x) + 6 f(\frac{1}{x}) = x + 5$,then the value of $\frac{d}{dx} (x^2 f(x))$ at $x = 1$ is

Let $f(x) = (x^x)^x$ and $g(x) = x^{(x^x)}$,then: