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Beliebt Rechnen >

(\partial)/(\partial x)(ysqrt(1+x^7))

Lösung

\frac{\partial}{\partial x} (y 1 + x^{7})

Lösung

\frac{7 y x ^{6}}{2 1 + x ^{7}}

Schritte zur Lösung

\frac{\partial}{\partial x} (y 1 + x^{7})

Behandle

y

als Konstante

Entferne die Konstante:

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

= y \frac{\partial}{\partial x} (1 + x^{7})

Wende die Kettenregel an:

\frac{1}{2 1 + x ^{7}} \frac{\partial}{\partial x} (1 + x^{7})

= \frac{1}{2 1 + x ^{7}} \frac{\partial}{\partial x} (1 + x^{7})

\frac{\partial}{\partial x} (1 + x^{7}) = 7 x^{6}

= y \frac{1}{2 1 + x ^{7}} \cdot 7 x^{6}

Vereinfache

y \frac{1}{2 1 + x ^{7}} \cdot 7 x^{6} : \frac{7 y x ^{6}}{2 1 + x ^{7}}

= \frac{7 y x ^{6}}{2 1 + x ^{7}}

Beliebte Beispiele

integral of (11x^2)/((144+x^2)^2)

\int \frac{11 x ^{2}}{( 144 + x ^{2} ) ^{2}} d x

derivative of x^6ln(7x)

\frac{d}{d x} (x^{6} ln (7 x))

derivative y= 1/((x^2-1)(x^2+3x+3))

d er i v a t i v e y = \frac{1}{( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 )}

derivative of x^{9/4}

\frac{d}{d x} (x^{\frac{9}{4}})

derivative f(θ)=sqrt(11θ)

d er i v a t i v e f (θ) = 11 θ