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Beliebt Rechnen >

derivative 6x^2sin(x)tan(x)

Lösung

ableitung von

6 x^{2} sin (x) tan (x)

Lösung

6 (2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2})

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} sin (x) tan (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (x^{2} sin (x) tan (x))

Wende die Produktregel an:

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

f = x^{2}, g = sin (x) tan (x)

= 6 (\frac{d}{d x} (x^{2}) sin (x) tan (x) + \frac{d}{d x} (sin (x) tan (x)) x^{2})

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

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

= 6 (2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2})

Graph

Beliebte Beispiele

implicit (dy)/(dx),x=y^2

im pl i c i t \frac{d y}{d x}, x = y^{2}

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\frac{d}{d x} (\frac{400}{x})

(dy)/(dx)=(x^2-7)/(15y^2)

\frac{d y}{d x} = \frac{x ^{2} - 7}{15 y ^{2}}

derivative of 3x^2+4x-1

\frac{d}{d x} (3 x^{2} + 4 x - 1)

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