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Beliebt Rechnen >

derivative of (sin(t)/(sqrt(1+x^2)))

Lösung

\frac{d}{d x} (\frac{sin ( t )}{1 + x ^{2}})

Lösung

- \frac{x sin ( t )}{( 1 + x ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( t )}{1 + x ^{2}})

Behandle

t

als Konstante

Entferne die Konstante:

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

= sin (t) \frac{d}{d x} (\frac{1}{1 + x ^{2}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= sin (t) \frac{d}{d x} ((1 + x^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 1 + x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x^{2})

= - \frac{1}{2 ( 1 + x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 + x^{2})

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

= sin (t) (- \frac{1}{2 ( 1 + x ^{2} ) ^{\frac{3}{2}}} \cdot 2 x)

Vereinfache

sin (t) (- \frac{1}{2 ( 1 + x ^{2} ) ^{\frac{3}{2}}} \cdot 2 x) : - \frac{x sin ( t )}{( 1 + x ^{2} ) ^{\frac{3}{2}}}

= - \frac{x sin ( t )}{( 1 + x ^{2} ) ^{\frac{3}{2}}}

Graph

Beliebte Beispiele

integral of x^3e^{ax^4}

\int x^{3} e^{a x^{4}} d x

integral of (2(x^2+1))/(x(x^2+2))

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

limit as x approaches 4-of 1/(x^2-16)

x \to 4 - lim (\frac{1}{x ^{2} - 16})

integral of x/(sqrt((1-x^2)))

\int \frac{x}{( 1 - x ^{2} )} d x

tangent y=ln(x^2-4x+1),(4,0)

t an g e n t y = ln (x^{2} - 4 x + 1), (4, 0)