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Beliebt Rechnen >

derivative of sin(1-xcos^3(x))

Lösung

\frac{d}{d x} (sin (1 - x) cos^{3} (x))

Lösung

- cos^{3} (x) cos (1 - x) - 3 cos^{2} (x) sin (x) sin (1 - x)

Schritte zur Lösung

\frac{d}{d x} (sin (1 - x) cos^{3} (x))

Wende die Produktregel an:

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

f = sin (1 - x), g = cos^{3} (x)

= \frac{d}{d x} (sin (1 - x)) cos^{3} (x) + \frac{d}{d x} (cos^{3} (x)) sin (1 - x)

\frac{d}{d x} (sin (1 - x)) = - cos (1 - x)

\frac{d}{d x} (cos^{3} (x)) = - 3 cos^{2} (x) sin (x)

= (- cos (1 - x)) cos^{3} (x) + (- 3 cos^{2} (x) sin (x)) sin (1 - x)

Vereinfache

= - cos^{3} (x) cos (1 - x) - 3 cos^{2} (x) sin (x) sin (1 - x)

Graph

Beliebte Beispiele

derivative f(x)=(e^x)/(2+5x)

d er i v a t i v e f (x) = \frac{e ^{x}}{2 + 5 x}

sqrt(x)+(sqrt(y)dy)/(dx)=0

x + \frac{y d y}{d x} = 0

6y^'-2y=xy^4,y(0)=-2

6 y^{^{'}} - 2 y = x y^{4}, y (0) = - 2

derivative f(x)=(6x+16)/(x+3)

d er i v a t i v e f (x) = \frac{6 x + 16}{x + 3}

derivative of xsqrt(x)+x^2sqrt(x)

\frac{d}{d x} (x x + x^{2} x)