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Beliebt Rechnen >

derivative of f(x(1x^2-1))

Lösung

\frac{d}{d x} (f (x) (1 x^{2} - 1))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (f (x) (1 \cdot x^{2} - 1))

Vereinfache

f (x) (1 \cdot x^{2} - 1) : f (x) (x^{2} - 1)

= \frac{d}{d x} (f (x) (x^{2} - 1))

Wende die Produktregel an:

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

f = f (x), g = x^{2} - 1

= \frac{d}{d x} (f (x)) (x^{2} - 1) + \frac{d}{d x} (x^{2} - 1) f (x)

\frac{d}{d x} (x^{2} - 1) = 2 x

= \frac{d}{d x} (f (x)) (x^{2} - 1) + 2 x f (x)

Beliebte Beispiele

t a y l or tan (x)

(\partial)/(\partial x)(e^{8x-200})

\frac{\partial}{\partial x} (e^{8 x - 200})

d/(dz(t))(((x-1)z(t))/(2z(t)-4t+1))

\frac{d}{d z ( t )} (\frac{( x - 1 ) z ( t )}{2 z ( t ) - 4 t + 1})

y y^{^{'}} = t + t y

derivative-xsin(x)

d er i v a t i v e - x sin (x)