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Beliebt Rechnen >

derivative of sin^2(2x^3+2x^2)

Lösung

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

Lösung

sin (2 (2 x^{2} + 2 x^{3})) (4 x + 6 x^{2})

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sin (2 x^{3} + 2 x^{2})) = cos (2 x^{3} + 2 x^{2}) (6 x^{2} + 4 x)

= 2 sin (2 x^{3} + 2 x^{2}) cos (2 x^{3} + 2 x^{2}) (6 x^{2} + 4 x)

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= sin (2 (2 x^{2} + 2 x^{3})) (4 x + 6 x^{2})

Graph

Beliebte Beispiele

(\partial)/(\partial x)(6y^2-4y^3-3x^2+6xy)

\frac{\partial}{\partial x} (6 y^{2} - 4 y^{3} - 3 x^{2} + 6 x y)

tangent f(x)= 6/(5x+2),\at x=-1

t an g e n t f (x) = \frac{6}{5 x + 2}, at x = - 1

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d er i v a t i v e f (x) = arctan (x)

integral of 1/(sin(θ))

\int \frac{1}{sin ( θ )} d θ

integral of 1/(3x-3)

\int \frac{1}{3 x - 3} d x