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Beliebt Rechnen >

derivative r=(t^4+12)(t^6+8)

Lösung

ableitung von

r = (t^{4} + 12) (t^{6} + 8)

Lösung

\frac{d t}{d r} = \frac{1}{2 t ^{3} ( 5 t ^{6} + 36 t ^{2} + 16 )}

Schritte zur Lösung

r = (t^{4} + 12) (t^{6} + 8)

Behandle

t

wie

t (r)

Beide Seiten differenzieren:

1 = 10 t^{9} \frac{d t}{d r} + 72 t^{5} \frac{d t}{d r} + 32 t^{3} \frac{d t}{d r}

Isoliere

\frac{d t}{d r} : \frac{d t}{d r} = \frac{1}{2 t ^{3} ( 5 t ^{6} + 36 t ^{2} + 16 )}

\frac{d t}{d r} = \frac{1}{2 t ^{3} ( 5 t ^{6} + 36 t ^{2} + 16 )}

Beliebte Beispiele

derivative 3x^3y^2=17

d er i v a t i v e 3 x^{3} y^{2} = 17

derivative x^2y+y^2x=6

d er i v a t i v e x^{2} y + y^{2} x = 6

derivative x(x+i)+y(y-i)+i=13

d er i v a t i v e x (x + i) + y (y - i) + i = 13

derivative x^2=2+t

d er i v a t i v e x^{2} = 2 + t

derivative x=(1-y^2)^{1/2}

d er i v a t i v e x = (1 - y^{2})^{\frac{1}{2}}