(\partial)/(\partial x)(x^2cos(xln(y)))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x^{2}, g = cos (x ln (y))

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

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

Vereinfache

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

\int 2 x^{2} e^{2 x} d x

\frac{\partial}{\partial s} (s t)

t an g e n t x^{4} - 2 x^{3} + 5

\int_{0}^{t} x d x

\frac{d}{d x} (cos (3 x^{7} + 2))