RD Chapter 30 Derivatives Ex 30.5 Solutions
Question - 1 : - Differentiate the following functions with respect to x:
Answer - 1 : -
Let us consider
y =
We need to find dy/dx
We know that y is a fraction of two functions say u and v where,
u = x2 +1 and v = x + 1
∴ y= u/v
Now let us apply quotient rule of differentiation.
By using quotient rule, we get
Question - 2 : - 
Answer - 2 : -
Let us consider
y =
We need to find dy/dx
We know that y is a fraction of two functions say u and v where,
u = 2x – 1 and v = x2 +1
∴ y= u/v
Now let us apply quotient rule of differentiation.
By using quotient rule, we get
Question - 3 : - 
Answer - 3 : -
Let us consider
y = 
We need to find dy/dx
We know that y is a fraction of two functions say u and v where,
u = x + ex and v= 1 + log x
∴ y= u/v
Now let us apply quotient rule of differentiation.
By using quotient rule, we get
Question - 4 : - 
Answer - 4 : -
Let us consider
y =
We need to find dy/dx
We know that y is a fraction of two functions say u and v where,
u = ex – tanx and v = cot x – xn
∴ y= u/v
Now let us apply quotient rule of differentiation.
By using quotient rule, we get
Question - 5 : - 
Answer - 5 : -
Let us consider
y =
We need to find dy/dx
We know that y is a fraction of two functions say u and v where,
u = ax2 + bx +c and v = px2 + qx + r
∴ y= u/v
Now let us apply quotient rule of differentiation.
By using quotient rule, we get
