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Online Notes / Calculus I (Practice Problems) / Derivatives / Implicit Differentiation

Chain Rule Calculus I - Practice Problems Related Rates

For problems 1  3 do each of the following.

(a)   Find  by solving the equation for y and differentiating directly.

(b)   Find  by implicit differentiation.

(c)    Check that the derivatives in (a) and (b) are the same.

 

1.  [Solution]

 

2.  [Solution]

 

3.  [Solution]

 

For problems 4  9 find  by implicit differentiation.

 

4.  [Solution]

 

5.  [Solution]

 

6.  [Solution]

 

7.  [Solution]

 

8.  [Solution]

 

9.  [Solution]

 

For problems 10 & 11 find the equation of the tangent line at the given point.

 

10.  at . [Solution]

 

11.  at . [Solution]

 

For problems 12 & 13 assume that ,  and  and differentiate the given equation with respect to t.

 

12.  [Solution]

 

13.  [Solution]

 

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Chain Rule Calculus I - Practice Problems Related Rates

Online Notes / Calculus I (Practice Problems) / Derivatives / Implicit Differentiation

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