What is derivative of 3x^2+2x^2y^3-1.25y^2=0 ?

The answer to derivative of 3x^2+2x^2y^3-1.25y^2=0 is (dy)/(dx)=-(4x(2y^3+3))/(y(12x^2y-5))

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derivative of 3x^2+2x^2y^3-1.25y^2=0

derivative of

3 x^{2} + 2 x^{2} y^{3} - 1.25 y^{2} = 0

\frac{d y}{d x} = - \frac{4 x ( 2 y ^{3} + 3 )}{y ( 12 x ^{2} y - 5 )}

Solution steps

3 x^{2} + 2 x^{2} y^{3} - 1.25 y^{2} = 0

Treat

y

y (x)

Differentiate both sides:

6 x + 2 (2 x y^{3} + 3 y^{2} \frac{d y}{d x} x^{2}) - 2.5 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{4 x ( 2 y ^{3} + 3 )}{y ( 12 x ^{2} y - 5 )}

\frac{d y}{d x} = - \frac{4 x ( 2 y ^{3} + 3 )}{y ( 12 x ^{2} y - 5 )}

(- 23, 2)

f (x) = ln (x^{2} + 1)

4 x - y = 1

y = arctan (x)

What is derivative of 3x^2+2x^2y^3-1.25y^2=0 ?
The answer to derivative of 3x^2+2x^2y^3-1.25y^2=0 is (dy)/(dx)=-(4x(2y^3+3))/(y(12x^2y-5))