(\partial)/(\partial x)((10x)/(36+x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{10 x}{36 + x ^{2} + y ^{2}})

\frac{10 ( - x ^{2} + y ^{2} + 36 )}{( 36 + x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{10 x}{36 + x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 10 \frac{\partial}{\partial x} (\frac{x}{36 + x ^{2} + y ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 10 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( 36 + x ^{2} + y ^{2} ) - \frac{\partial}{\partial x} ( 36 + x ^{2} + y ^{2} ) x}{( 36 + x ^{2} + y ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (36 + x^{2} + y^{2}) = 2 x

= 10 \cdot \frac{1 \cdot ( 36 + x ^{2} + y ^{2} ) - 2 xx}{( 36 + x ^{2} + y ^{2} ) ^{2}}

Vereinfache

10 \cdot \frac{1 \cdot ( 36 + x ^{2} + y ^{2} ) - 2 xx}{( 36 + x ^{2} + y ^{2} ) ^{2}} : \frac{10 ( - x ^{2} + y ^{2} + 36 )}{( 36 + x ^{2} + y ^{2} ) ^{2}}

= \frac{10 ( - x ^{2} + y ^{2} + 36 )}{( 36 + x ^{2} + y ^{2} ) ^{2}}

n = 1 \sum \infty \frac{1 0 ^{n}}{n ^{n}}

\frac{\partial}{\partial x} (e^{x y} + 2 x - 5 y)

y^{^{''}} + 8 y^{^{'}} + 7 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

\frac{d ^{2}}{d x ^{2}} (x^{4} - 6 x^{3})

\frac{\partial}{\partial x} (\frac{7 x}{x ^{2} + y ^{2}})