derivative of sin(x^{tan(x}))

Lösung

\frac{d}{d x} (sin (x^{t a n (x)}))

x^{t a n (x)} cos (x^{t a n (x)}) (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (sin (x^{t a n (x)}))

Wende die Kettenregel an:

cos (x^{t a n (x)}) \frac{d}{d x} (x^{t a n (x)})

= cos (x^{t a n (x)}) \frac{d}{d x} (x^{t a n (x)})

\frac{d}{d x} (x^{t a n (x)}) = e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

= cos (x^{t a n (x)}) e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

e^{t a n (x) l n (x)} = x^{t a n (x)}

= x^{t a n (x)} cos (x^{t a n (x)}) (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

(2 x + 1) y^{^{'}} + 2 y = 4 x, y (0) = 1

\frac{\partial}{\partial z} (ln (x^{2} + y^{4}) - z)

25 y^{^{''}} - y = x e^{\frac{x}{5}}, y (0) = 1, y^{^{'}} (0) = 0

x \to \infty lim (\frac{1}{x ( ln ( x ) ) ^{4}})

\int_{1}^{3} 1 + (x^{3} - \frac{1}{4 x ^{3}})^{2} d x