Differentiating implicitly

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Differentiating implicitly

• Adrian Sparrow www.ibmaths.com

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Differentiate y w.r.t. x
look at what y differentiates with respect to x
What about y2?
Now try and differentiate the following with
respect to x
check your answers with your teacher
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Put this into practice
Differentiate the following equation w.r.t. x
giving the gradient function in terms of x and y.
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Some questions. Differentiate w.r.t. x
1. 2. 3. 4. 5.
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Applying the product rule for differentiating
Differentiate w.r.t. x
Use the product rule
and
So,
Now try
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More practice questions. Differentiate w.r.t. x
1. 2. 3. 4. 5.
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Finding the gradient of an implicit function
Find the equation of the tangent to the curve
at the point
At the point x1, y-1, find the gradient.
so, equation of the line is
Substituting in the values of x and y, and c1.