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Beliebt Rechnen >

(\partial)/(\partial x)(cos^4(x^3y^5))

Lösung

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{5}))

Lösung

- 12 x^{2} y^{5} cos^{3} (x^{3} y^{5}) sin (x^{3} y^{5})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{5}))

Behandle

y

als Konstante

Wende die Kettenregel an:

4 (cos (x^{3} y^{5}))^{3} \frac{\partial}{\partial x} (cos (x^{3} y^{5}))

= 4 (cos (x^{3} y^{5}))^{3} \frac{\partial}{\partial x} (cos (x^{3} y^{5}))

\frac{\partial}{\partial x} (cos (x^{3} y^{5})) = - sin (x^{3} y^{5}) \cdot 3 y^{5} x^{2}

= 4 (cos (x^{3} y^{5}))^{3} (- sin (x^{3} y^{5}) \cdot 3 y^{5} x^{2})

Vereinfache

= - 12 x^{2} y^{5} cos^{3} (x^{3} y^{5}) sin (x^{3} y^{5})

Beliebte Beispiele

limit as x approaches-8 of x^2-3

x \to - 8 lim (x^{2} - 3)

derivative f(x)=4x^3-8x

d er i v a t i v e f (x) = 4 x^{3} - 8 x

derivative ae^{bt}

d er i v a t i v e a e^{b t}

tangent f(x)= 3/(x+2),\at x=3

t an g e n t f (x) = \frac{3}{x + 2}, at x = 3

derivative sin(9x)+cos(2x)

d er i v a t i v e sin (9 x) + cos (2 x)