derivative of sin(x/(1+y))

Lösung

\frac{d}{d x} (sin (\frac{x}{1 + y}))

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

Schritte zur Lösung

\frac{d}{d x} (sin (\frac{x}{1 + y}))

Wende die Kettenregel an:

cos (\frac{x}{1 + y}) \frac{d}{d x} (\frac{x}{1 + y})

= cos (\frac{x}{1 + y}) \frac{d}{d x} (\frac{x}{1 + y})

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (5 π cos (π x))

\int_{- 2}^{3} \frac{38}{x ^{4}} d x

x \to - 2 lim (- x^{3} + x)

t an g e n t f (x) = \frac{x}{( 1 + x ^{2} )}, at x = 3

\int_{- 3}^{- 1} (x^{2} - 4 x + 8) d x