(\partial)/(\partial x)(cos^3(x^3y^8))

Lösung

\frac{\partial}{\partial x} (cos^{3} (x^{3} y^{8}))

- 9 x^{2} y^{8} cos^{2} (x^{3} y^{8}) sin (x^{3} y^{8})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{3} (x^{3} y^{8}))

Behandle

y

als Konstante

Wende die Kettenregel an:

3 (cos (x^{3} y^{8}))^{2} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

= 3 (cos (x^{3} y^{8}))^{2} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

\frac{\partial}{\partial x} (cos (x^{3} y^{8})) = - sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2}

= 3 (cos (x^{3} y^{8}))^{2} (- sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2})

Vereinfache

= - 9 x^{2} y^{8} cos^{2} (x^{3} y^{8}) sin (x^{3} y^{8})

y^{^{''}} + 5 y^{^{'}} + 6 y = 4 e^{- 2 t}

(1 + \frac{3}{y} + x) \frac{d y}{d x} + y = \frac{3}{x} - 1

\int sin (4 π x) d x

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

t a y l or cos (3 x), 0