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Beliebt Rechnen >

derivative of 2xsec(x)

Lösung

\frac{d}{d x} (2 x sec (x))

Lösung

2 (sec (x) + x sec (x) tan (x))

Schritte zur Lösung

\frac{d}{d x} (2 x sec (x))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x sec (x))

Wende die Produktregel an:

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

f = x, g = sec (x)

= 2 (\frac{d x}{d x} sec (x) + \frac{d}{d x} (sec (x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 2 (1 \cdot sec (x) + sec (x) tan (x) x)

Vereinfache

= 2 (sec (x) + x sec (x) tan (x))

Graph

Beliebte Beispiele

derivative of (x+2^x)

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

integral of ((2+e^x)^2)/(e^x)

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

x y^{^{'}} + 3 y = x^{4} - x

integral of (e^x)/((5-e^x)^2)

\int \frac{e ^{x}}{( 5 - e ^{x} ) ^{2}} d x

integral of 1/(v^2-v+1)

\int \frac{1}{v ^{2} - v + 1} d v