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11.(vii)   Find the derivative of the following functions:

Given  As we know  the property  Applying this property,

11(vi)   Find the derivative of the following functions:

Given, Now as we know the property  So, applying the property,

11.(v)   Find the derivative of the following functions:

Given, As we know  the property  Applying the property,   Now As we know the quotient rule of derivative, So applying this rule, we get

11.(iv)     Find the derivative of the following functions:

Given : Now As we know the quotient rule of derivative, So applying this rule, we get

11 (iii)   Find the derivative of the following functions:

Given As we know the property  Applying the property, we get

11(ii)   Find the derivative of the following functions:

Given Now As we know the quotient rule of derivative, So applying this rule, we get

11.(i)   Find the derivative of the following functions:

Given, f(x)= Now, As we know the product rule of derivative, So, applying the rule here,

10.   Find the derivative of from first principle.

Given,  f(x)= Now, As we know, The derivative of any function at x is

9(vi)   Find the derivative of

Given As we know the quotient rule of derivative: and the property  So applying this rule, we get Hence

9(v)   Find the derivative of

Given As we know, the property, and the property  applying that property we get

9.(iv)   Find the derivative of

Given As we know, the property, and the property  applying that property we get

9(iii)   Find the derivative of

Given As we know, the property, and the property  applying that property we get

9.(ii)   Find the derivative of

Given. As we know, the property, and the property  applying that property we get

9.(i)   Find the derivative of

Given: As we know, the property, and the property  applying that property we get

8.   Find the derivative of  for some constant a.

Given, Now As we know the quotient rule of derivative, So applying this rule, we get Hence

7.(iii)   For some constants a and b, find the derivative of

Given, Now As we know the quotient rule of derivative, So applying this rule, we get Hence

7.(ii)   For some constants a and b, find the derivative of

Given  As we know, the property, and the property  applying those properties we get

7.(i)  For some constants a and b, find the derivative of

Given As we know, the property, and the property  applying that property we get

6.   Find the derivative of  for some fixed real number a.

Given  As we know, the property, applying that property we get

5.   For the function  Prove that f '(1) =100 f '(0).

As we know, the property, applying that property we get  Now. So, Here   Hence Proved.
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