Assignments

The central theme of the following assignments is to calculate the derivative of an implicitly defined function y(x).

1. Calculate y' if:

(2x+1)(1+y)-1=0

Solution

2. Calculate y' if:

(x^3-1)(1+y)=3

Solution

3. Calculate y' if:

\displaystyle\frac{x}{y+1}=2

Solution

4. Calculate y' if:

x\ln(y)-4=0

Solution

5. Calculate the tangent line at the point (0,0) of the graph of the following expression:

(x+1)e^y-1=0

Solution

6. Calculate the tangent line at the point  (1,3) of the graph of the following expression:

2x+3y^2=29

Solution

7. Calculate y'' if:

xy=5

Solution

8. If y is a differentiable function of x satisfying the following equation:

2x^2+6xy+y^2=18

calculate y'.

Solution

9. Calculate the tangent line at the point (1,4) of the graph of the following expression:

-x+3^{\sqrt{y}}=8

Solution

10. The equation:

x^2y^3+(y+1)e^{-x}=x+2

defines y as a differentiable function of x close to the point (x,y)=(0,1).

Calculate the tangent line of the graph at this point.

Solution

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