CameraIcon

SearchIcon

MyQuestionIcon

1

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

Chain Rule of Differentiation

Differentiate...

Question

Differentiate:
${sin}^{2} y + cos x y = K$

Open in App

Solution

$\frac{d y}{d x} o f {s i n}^{2} y + C o s x y = π$

$2 S i n x (C o s x y \frac{d y}{d x}) - S i n x y (y + \frac{x d y}{d x}) = 0$

$2 S i n y C o s y \frac{d y}{d x} = S i n x y (y + x \frac{d y}{d x})$

${S i n}^{2} y \frac{d y}{d x} = y S i n x y + x S i n x y \frac{d y}{d x}$

Hence ,

$\frac{d y}{d x} = \frac{y S i n x y}{S i n 2 y} - x S i n x y$

The same value of $\frac{d y}{d x S i n y}$ and $\frac{d y}{d x C o s y}$ will be obtained if using logs on both the sides .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Differentiate :

{sin}^{2} y + cos x y = κ

\frac{d y}{d x}

{sin}^{2} y + cos x y = k

\frac{d y}{d x}

x = 1, y = \frac{π}{4}

{sin}^{2} y + cos x y = k

{sin}^{2} y + cos (x y) = π

\frac{d y}{d x}

Q. Find the solution of the differential equation:

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

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Basic Theorems in Differentiation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Chain Rule of Differentiation

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon