(\partial)/(\partial x)(e^{-sin^2(x)}(x+c))

Lösung

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

- e^{- s i n^{2} (x)} sin (2 x) (x + c) + e^{- s i n^{2} (x)}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

Wende die Produktregel an:

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

f = e^{- s i n^{2} (x)}, g = x + c

= \frac{\partial}{\partial x} (e^{- s i n^{2} (x)}) (x + c) + \frac{\partial}{\partial x} (x + c) e^{- s i n^{2} (x)}

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)}) = - e^{- s i n^{2} (x)} sin (2 x)

\frac{\partial}{\partial x} (x + c) = 1

= (- e^{- s i n^{2} (x)} sin (2 x)) (x + c) + 1 \cdot e^{- s i n^{2} (x)}

Vereinfache

= - e^{- s i n^{2} (x)} sin (2 x) (x + c) + e^{- s i n^{2} (x)}

\int x x^{\frac{3}{2} - 1} d x

\frac{d}{d x} ((x + 6)^{\frac{2}{3}})

y^{^{''}} + 25 y = 0.5 sin (5 t), y (0) = 0, y^{^{'}} (0) = 0

x \to 3 lim (3 - x)

d er i v a t i v e \frac{( 4 + h ) ^{2} - 16}{h}