What is derivative of r=(t^4+12)(t^6+8) ?

The answer to derivative of r=(t^4+12)(t^6+8) is (dt)/(dr)= 1/(2t^3(5t^6+36t^2+16))

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

derivative of

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

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

Solution steps

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

Treat

t

t (r)

Differentiate both sides:

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}

Isolate

\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 )}

What is derivative of r=(t^4+12)(t^6+8) ?
The answer to derivative of r=(t^4+12)(t^6+8) is (dt)/(dr)= 1/(2t^3(5t^6+36t^2+16))