derivative of sin(xcos(y))

Lösung

\frac{d}{d x} (sin (x) cos (y))

cos (y) cos (x) - sin (y) sin (x) \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (sin (x) cos (y))

Wende die Produktregel an:

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

f = sin (x), g = cos (y)

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

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (cos (y)) = - sin (y) \frac{d y}{d x}

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

Vereinfache

= cos (y) cos (x) - sin (y) sin (x) \frac{d y}{d x}

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

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

\int \frac{1}{64 e ^{- 7 x} + e ^{7 x}} d x

x \to 0 lim (\frac{5}{x + x ^{2}})

d er i v a t i v e f (x) = 10 x + 6