derivative of h({g}(xk(x)))

Lösung

\frac{d}{d x} (h (g (x) k (x)))

hk (x \frac{d}{d x} (g (x)) + g (x))

Schritte zur Lösung

\frac{d}{d x} (h (g (x) k (x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= hk \frac{d}{d x} (g (x) x)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = g (x), g = x

= hk (\frac{d}{d x} (g (x)) x + \frac{d x}{d x} g (x))

\frac{d x}{d x} = 1

= hk (\frac{d}{d x} (g (x)) x + 1 \cdot g (x))

Vereinfache

= hk (x \frac{d}{d x} (g (x)) + g (x))

\int (x^{3} + 4 x)^{2} (3 x^{2} + 4) d x

\int \frac{x ^{3} + 7}{x ^{2} + 5 x + 6} d x

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

\frac{d}{d x} (\frac{x ^{2} + 2 x}{( x + 1 ) ^{2}})

d er i v a t i v e y = a^{4} + cos^{4} (x)