(\partial)/(\partial x)(xcos(pix*y^2))

Lösung

\frac{\partial}{\partial x} (x \cdot cos (π \cdot x \cdot y^{2}))

cos (π x y^{2}) - π x y^{2} sin (π x y^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (x cos (π x y^{2}))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = cos (π x y^{2})

= \frac{\partial}{\partial x} (x) cos (π x y^{2}) + \frac{\partial}{\partial x} (cos (π x y^{2})) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (cos (π x y^{2})) = - sin (π x y^{2}) π y^{2}

= 1 \cdot cos (π x y^{2}) + (- sin (π x y^{2}) π y^{2}) x

Vereinfache

= cos (π x y^{2}) - π x y^{2} sin (π x y^{2})

\int \frac{1}{x} 1 + \frac{1}{x ^{4}} d x

y^{^{''}} + 4 y^{^{'}} + 3 y = 32 x e^{x}

\frac{d}{d x} (3 x (18 x^{4} + \frac{13}{x + 1}))

\frac{d}{d x} (ln (sin (x^{3})))

t an g e n t x y = - 121