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Differential Calculus

Differentiation and Derivatives

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Problem Name

Problem Description

Notes

derivative_41

Find the derivative of the following function. Then evaluate the derivative for the given value of the independent variable.
derivative_41_1.gif; evaluate derivative_41_2.gif when derivative_41_3.gif.

 

derivative_42

Find the derivative of the following function. Then evaluate the derivative for the given value of the independent variable.
derivative_42_1.gif; evaluate derivative_42_2.gif when derivative_42_3.gif.

 

derivative_43

Find the formula for the derivative with respect to derivative_43_1.gif for the function. (Treat derivative_43_2.gif, derivative_43_3.gif, and derivative_43_4.gif as constants.)
derivative_43_5.gif

 

derivative_44

Find the formula for the derivative with respect to derivative_44_1.gif for the function. (Treat derivative_44_2.gif, derivative_44_3.gif, and derivative_44_4.gif as constants.)
derivative_44_5.gif

 

derivative_45

Find the formula for the derivative with respect to derivative_55_1.gif for the function. (Treat derivative_55_2.gif, derivative_55_3.gif, and derivative_55_4.gif as constants.)
derivative_55_5.gif

 

derivative_46

Find the formula for the derivative with respect to derivative_46_1.gif for the function. (Treat derivative_46_2.gif, derivative_46_3.gif, and derivative_46_4.gif as constants.)
derivative_46_5.gif

 

derivative_47

Find the formula for the derivative with respect to derivative_47_1.gif for the function. (Treat derivative_47_2.gif, derivative_47_3.gif, and derivative_47_4.gif as constants.)
derivative_47_5.gif

 

derivative_48

If derivative_48_1.gif, where derivative_48_2.gif is a constant and derivative_48_3.gif is a function of derivative_48_4.gif, then use the definition of the derivative to prove that derivative_48_5.gif.

 

derivative_49

Write an expression for derivative_49_1.gif for the function derivative_49_2.gif. (derivative_49_3.gif). Then use the definition of the derivative to find derivative_49_4.gif.

 

derivative_50

Using the definition of the derivative, show that, if derivative_50_1.gif, then derivative_50_2.gif.

 

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