derivative of x^3sinh^2(x+cosh^2(x^3))

Lösung

\frac{d}{d x} (x^{3} sinh^{2} (x) + cosh^{2} (x^{3}))

3 x^{2} sinh^{2} (x) + 2 sinh (x) cosh (x) x^{3} + 6 x^{2} cosh (x^{3}) sinh (x^{3})

Schritte zur Lösung

\frac{d}{d x} (x^{3} sinh^{2} (x) + cosh^{2} (x^{3}))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3} sinh^{2} (x)) + \frac{d}{d x} (cosh^{2} (x^{3}))

\frac{d}{d x} (x^{3} sinh^{2} (x)) = 3 x^{2} sinh^{2} (x) + 2 sinh (x) cosh (x) x^{3}

\frac{d}{d x} (cosh^{2} (x^{3})) = 6 x^{2} cosh (x^{3}) sinh (x^{3})

= 3 x^{2} sinh^{2} (x) + 2 sinh (x) cosh (x) x^{3} + 6 x^{2} cosh (x^{3}) sinh (x^{3})

a re a x = 9, x = y^{2}

\int 12 x + 12 d x

\int \frac{e ^{4 x} + 4 e ^{x} + 8}{e ^{x}} d x

\int x^{5} e^{- x} d x

t an g e n t f (x) = \frac{5}{x}, at x = 2