(\partial)/(\partial x)(log_{3}(7^{x^2-4}))

Lösung

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

2 lo g_{3} (7) x

Schritte zur Lösung

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

Vereinfache

lo g_{3} (7^{x^{2} - 4}) : lo g_{3} (7) (x^{2} - 4)

= \frac{\partial}{\partial x} (lo g_{3} (7) (x^{2} - 4))

Entferne die Konstante:

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

= lo g_{3} (7) \frac{\partial}{\partial x} (x^{2} - 4)

Wende die Summen-/Differenzregel an:

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

= lo g_{3} (7) (\frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (4) = 0

= lo g_{3} (7) (2 x - 0)

Vereinfache

= 2 lo g_{3} (7) x

\int_{0}^{5} (5 x^{2} - x^{3}) d x

\int \frac{5}{4 - 3 x} d x

\int (ln (x))^{2} \frac{1}{x ^{2}} d x

\frac{\partial}{\partial x} (sin (5 x y + 4 yz + 7 x z))

t an g e n t f (x) = \frac{- 8 x}{x ^{2} + 1}, (0, 0)