(\partial)/(\partial y)(xsqrt(1+y^5))

Lösung

\frac{\partial}{\partial y} (x 1 + y^{5})

\frac{5 x y ^{4}}{2 1 + y ^{5}}

Schritte zur Lösung

\frac{\partial}{\partial y} (x 1 + y^{5})

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (1 + y^{5})

Wende die Kettenregel an:

\frac{1}{2 1 + y ^{5}} \frac{\partial}{\partial y} (1 + y^{5})

= \frac{1}{2 1 + y ^{5}} \frac{\partial}{\partial y} (1 + y^{5})

\frac{\partial}{\partial y} (1 + y^{5}) = 5 y^{4}

= x \frac{1}{2 1 + y ^{5}} \cdot 5 y^{4}

Vereinfache

x \frac{1}{2 1 + y ^{5}} \cdot 5 y^{4} : \frac{5 x y ^{4}}{2 1 + y ^{5}}

= \frac{5 x y ^{4}}{2 1 + y ^{5}}

\int t e^{- a t} d t

6 t^{2} y^{^{''}} - 12 y = 14 t^{2} - 1

\int 4 x^{3} - 10 x d x

\int \frac{4 t ^{3} - t ^{2} + 16 t}{t ^{2} + 4} d t

y^{^{'}} - 2 x y = 8 x