derivative of x^3-ysinh(x^2)

Lösung

\frac{d}{d x} (x^{3} - y sinh (x^{2}))

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

Schritte zur Lösung

\frac{d}{d x} (x^{3} - y sinh (x^{2}))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (y sinh (x^{2}))

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

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

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

Vereinfache

3 x^{2} - (\frac{d y}{d x} sinh (x^{2}) + cosh (x^{2}) \cdot 2 x y) : 3 x^{2} - sinh (x^{2}) \frac{d y}{d x} - 2 x cosh (x^{2}) y

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

\int_{- 1}^{1} \frac{1}{x ^{5}} d x

\frac{\partial}{\partial x} (7 e^{x} \cdot sin (y))

n = 1 \sum \infty \frac{1}{2 n ln ( n )}

\int 3 x^{2} + 4 x + 1 d x

\frac{d y}{d x} + \frac{1}{x + 4} y = x^{- 2}