Ratkaise d/dx(sinx^tanx)

$$\frac { d } { d x } ( \sin x ^ { \tan x } )$$

Laske

$$\frac{\left(2x\ln(x)+\sin(2x)\right)\cos(x^{\tan(x)})x^{\tan(x)-1}}{2\left(\cos(x)\right)^{2}}$$

Derivoi muuttujan x suhteen

$$\frac{x^{\tan(x)-2}\left(-4\ln(x)\sin(2x)\sin(x^{\tan(x)})x^{\frac{\sin(x)+\cos(x)}{\cos(x)}}-4\ln(x)^{2}\sin(x^{\tan(x)})x^{\frac{\sin(x)+2\cos(x)}{\cos(x)}}-\left(\sin(2x)\right)^{2}x^{\tan(x)}\sin(x^{\tan(x)})+4\cos(x^{\tan(x)})\left(x\ln(x)\right)^{2}+4x^{2}\ln(x)\sin(2x)\cos(x^{\tan(x)})-4\sin(x)\left(\cos(x)\right)^{3}\cos(x^{\tan(x)})+\left(\sin(2x)\right)^{2}\cos(x^{\tan(x)})+4x\ln(x)\sin(2x)\cos(x^{\tan(x)})+8x\left(\cos(x)\right)^{2}\cos(x^{\tan(x)})\right)}{4\left(\cos(x)\right)^{4}}$$