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10.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

$\frac{a}{x^4} - \frac{b}{x^2 } + \cos x$

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

9.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

$\frac{px^2 + qx + r }{ax +b }$

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

8.   Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

$\frac{ax + b }{px^2 + qx + r }$

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

7.   Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

$\frac{1 }{ax ^2 + bx + c}$

Given, Now, As we know the derivative of any such  function  is given by  Hence, The derivative of f(x) is

6.   Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

$\frac{1 + \frac{1}{x}}{1- \frac{1}{x}}$

Given, Also can be written as  Now, As we know the derivative of any function   Hence, The derivative of f(x) is  Hence Derivative of the function is

5.   Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $ax + b / cx + d$

Given, Now, As we know the derivative of any function   Hence, The derivative of f(x) is  Hence Derivative of the function is  .

4.   Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $( ax + b ) ( cx + d )^2$

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

3.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\left(px + q\right) \left ( \frac{r}{x}+ s \right )$

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

2.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):  (x+a )

Given  f(x)= x + a As we know, the property, applying that property we get

1.(iv)   Find the derivative of the following functions from first principle: $\cos ( x - \pi /8 )$

Given. Now, As we know, The derivative of any function at x is

1.(iii)   Find the derivative of the following functions from first principle: $\sin ( x+1)$

Given. Now, As we know, The derivative of any function at x is

1.(ii)   Find the derivative of the following functions from first principle: $( - x ) ^{-1}$

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

1(i)   Find the derivative of the following functions from first principle: -x

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

11.(vii)   Find the derivative of the following functions:  $2 \tan x - 7 \sec x$

Given  As we know  the property  Applying this property,

11(vi)   Find the derivative of the following functions: $5 \sin x - 6 \cos x + 7$

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

11.(v)   Find the derivative of the following functions:  $3 \cot x + 5 \csc x$

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:  $\csc x$

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: $5 \sec x + 4 \cos x$

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

11(ii)   Find the derivative of the following functions:  $\sec x$

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: $\sin x \cos x$

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