What is derivative of x=((1+t)^3)/(t^2) ?

The answer to derivative of x=((1+t)^3)/(t^2) is (dt)/(dx)=(t^3)/((t+1)^2(t-2))

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derivative of x=((1+t)^3)/(t^2)

derivative of

x = \frac{( 1 + t ) ^{3}}{t ^{2}}

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

Solution steps

x = \frac{( 1 + t ) ^{3}}{t ^{2}}

Treat

t

t (x)

Differentiate both sides:

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

Isolate

\frac{d t}{d x} : \frac{d t}{d x} = \frac{t ^{3}}{( t + 1 ) ^{2} ( t - 2 )}

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

y^{2} = 2 x

x^{2} y^{2} = 1

x = (t^{2} + 1)^{\frac{1}{2}}

x + y - x^{3} y = 15

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

What is derivative of x=((1+t)^3)/(t^2) ?
The answer to derivative of x=((1+t)^3)/(t^2) is (dt)/(dx)=(t^3)/((t+1)^2(t-2))