Answer

Verified

456k+ views

**Hint**: If u and v are functions in terms of x then their differentiation with respect to x is given by\[\dfrac{d}{dx}\left( uv \right)=u\times \dfrac{dv}{dx}+v\times \dfrac{du}{dx}\]and this formula is called as the product rule. Use the product rule to simplify the given equation and calculate the derivative of the equation.

**:**

__Complete step-by-step answer__We know the differentiation with respect to x for two functions u and v in terms of x is given by \[\dfrac{d}{dx}\left( uv \right)=u\times \dfrac{dv}{dx}+v\times \dfrac{du}{dx}\].

Applying the above mentioned formula to simplify the given equation.

First apply derivative on both sides of the equation with respect to x then we will get

\[\dfrac{d}{dx}\left( {{y}^{2}} \right)-3\dfrac{d}{dx}\left( xy \right)+\dfrac{d}{dx}\left( {{x}^{2}} \right)=\dfrac{d}{dx}\left( x \right)\]

Using the formula for derivative of \[{{u}^{n}}\] in terms of u is given by \[\dfrac{d}{du}\left( {{u}^{n}} \right)=n{{u}^{n-1}}\] where n is any integer and u is any variable we get,

We know the differentiation of x with respect to x is 1.

\[2y\dfrac{dy}{dx}-3\left( x\times \dfrac{dy}{dx}+y \right)+2x=1\]

Simplifying the equation we get,

\[2y\dfrac{dy}{dx}-3x\dfrac{dy}{dx}+3y+2x=1\]

Subtracting with 3y and 2x on both sides we get,

\[2y\dfrac{dy}{dx}-3x\dfrac{dy}{dx}=1-3y-2x\]

Taking \[\dfrac{dy}{dx}\] as common in the LHS we get,

\[\dfrac{dy}{dx}\left( 2y-3x \right)=1-3y-2x\]

On dividing with (2y - 3x) on both sides we get,

\[\dfrac{dy}{dx}=\dfrac{1-3y-2x}{2y-3x}\]

Hence, we get the derivative of the equation \[{{y}^{2}}-3xy+{{x}^{2}}=x\] as \[\dfrac{dy}{dx}=\dfrac{1-3y-2x}{2y-3x}\].

**Note**: The formula for derivative of \[{{u}^{n}}\] in terms of u is given by \[\dfrac{d}{du}\left( {{u}^{n}} \right)=n{{u}^{n-1}}\] where n is any integer and u is any variable. The derivative of x component with respect to x is 1 and derivative of y component with respect to x is \[\dfrac{dy}{dx}\]. Using previously mentioned rules carefully complete the basic mathematical operations like addition, subtraction to calculate the final answer.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you graph the function fx 4x class 9 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE