(\partial)/(\partial x)(3(x-y)e^{3y+3x^2})

Lösung

\frac{\partial}{\partial x} (3 (x - y) e^{3 y + 3 x^{2}})

3 (e^{3 y + 3 x^{2}} + 6 e^{3 y + 3 x^{2}} x (x - y))

Schritte zur Lösung

\frac{\partial}{\partial x} (3 (x - y) e^{3 y + 3 x^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} ((x - y) e^{3 y + 3 x^{2}})

Wende die Produktregel an:

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

f = x - y, g = e^{3 y + 3 x^{2}}

= 3 (\frac{\partial}{\partial x} (x - y) e^{3 y + 3 x^{2}} + \frac{\partial}{\partial x} (e^{3 y + 3 x^{2}}) (x - y))

\frac{\partial}{\partial x} (x - y) = 1

\frac{\partial}{\partial x} (e^{3 y + 3 x^{2}}) = e^{3 y + 3 x^{2}} \cdot 6 x

= 3 (1 \cdot e^{3 y + 3 x^{2}} + e^{3 y + 3 x^{2}} \cdot 6 x (x - y))

Vereinfache

= 3 (e^{3 y + 3 x^{2}} + 6 e^{3 y + 3 x^{2}} x (x - y))

\frac{d}{d t} (cosh (t))

d er i v a t i v e cot^{2} (cos (θ))

\frac{d}{d x} ((3 x^{2} - 5)^{4} (2 x^{2} + 1)^{3})

d er i v a t i v e f (x) = tan (sec (cos (x)))

\frac{d}{d x} (tan^{s e c (\frac{1}{x})} (\frac{1}{x}))