(\partial)/(\partial x)(cos^3(x^7y^7))

Lösung

\frac{\partial}{\partial x} (cos^{3} (x^{7} y^{7}))

- 21 x^{6} y^{7} cos^{2} (x^{7} y^{7}) sin (x^{7} y^{7})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{3} (x^{7} y^{7}))

Behandle

y

als Konstante

Wende die Kettenregel an:

3 (cos (x^{7} y^{7}))^{2} \frac{\partial}{\partial x} (cos (x^{7} y^{7}))

= 3 (cos (x^{7} y^{7}))^{2} \frac{\partial}{\partial x} (cos (x^{7} y^{7}))

\frac{\partial}{\partial x} (cos (x^{7} y^{7})) = - sin (x^{7} y^{7}) \cdot 7 y^{7} x^{6}

= 3 (cos (x^{7} y^{7}))^{2} (- sin (x^{7} y^{7}) \cdot 7 y^{7} x^{6})

Vereinfache

= - 21 x^{6} y^{7} cos^{2} (x^{7} y^{7}) sin (x^{7} y^{7})

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

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

d er i v a t i v e f (x) = - 3 x^{3} + 2 x^{2} - 4 x + 7

\frac{d}{d x} (2.873 sec (x))

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