derivative of {f}(x\circ {g}(x))

Lösung

\frac{d}{d x} (f (x) \circ g (x))

\circ (\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x))

Schritte zur Lösung

\frac{d}{d x} (f (x) \circ g (x))

Entferne die Konstante:

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

= \circ \frac{d}{d x} (f (x) g (x))

Wende die Produktregel an:

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

f = f (x), g = g (x)

= \circ (\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x))

= \circ (\frac{d}{d x} (f (x)) g (x) + \frac{d}{d x} (g (x)) f (x))

x \to 1 - lim (\frac{x ^{3} - 1}{x - 1})

(x - 7)^{4} y^{^{'}} + 5 (x - 7)^{3} y = x + 7

\int \frac{1}{tan ( y )} d y

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 7} e^{4 t}

x \to 1 + lim (x^{2})