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Beliebt Rechnen >

derivative of sqrt((x+39^2+(43+x)^2))

Lösung

\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

Lösung

\frac{2 ( x + 41 )}{2 x ^{2} + 164 x + 3370}

Schritte zur Lösung

\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

Wende die Kettenregel an:

\frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} \frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

= \frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} \frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2}) = 4 x + 164

= \frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} (4 x + 164)

Vereinfache

\frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} (4 x + 164) : \frac{2 ( x + 41 )}{2 x ^{2} + 164 x + 3370}

= \frac{2 ( x + 41 )}{2 x ^{2} + 164 x + 3370}

Graph

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