MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Implicit Differentiation

Implict funct...

Question

Implict function $x^{3} + y^{3} = 3 a x y$

Open in App

Solution

$x^{3} + y^{3} = a x y$

By differentiating,

$3 x^{2} + 3 y^{2} \frac{d y}{d x} = a [x \frac{d y}{d x} + y (1)]$

$3 x^{2} + 3 y^{2} \frac{d y}{d x} = a x \frac{d y}{d x} + y a$

$\frac{d y}{d x} (3 y^{2} - a x) = a y - 3 x^{2}$

$\frac{d y}{d x} = \frac{a y - 3 x^{2}}{3 y^{2} - a x}$

Suggest Corrections

thumbs-up

0

Similar questions

x^{3} + y^{3} = 3 a x y

\frac{d y}{d x}

x^{3} + y^{3} = 3 a x y

\frac{d y}{d x}

Q. The symmetry in curve

x^{3} + y^{3} = 3 a x y

x^{3} + y^{3} - 3 a x y = 0

\frac{d y}{d x}

x^{3} + y^{3} - 3 a x y = 0

then prove that

\frac{d^{2} y}{d x^{2}} = \frac{2 a^{2} x y}{{(a x - y^{2})}^{3}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Implicit Differentiation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Implicit Differentiation

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon