Question

PROBLEM 1:
Differentiate the given functio
n f(x) = (√x + a)(3x2 – 5x + 7)
SOLUTION:

Step 2: Identify the dependent and independent variables in given function​

Answer 1

Given : f(x)  = (√x + a)(3x² – 5x + 7)

To Find : Differentiate the f(x)

Solution:

f(x)  = (√x + a)(3x² – 5x + 7)

=> f(x)  =√x (3x² – 5x + 7)  + a(3x² – 5x + 7)

f'(x)  =  √x(6x - 5)  + (1/2√x) (3x² – 5x + 7) + a(6x - 5)

= 6x√x - 5√x + 3x√x/2  - 5√x/2  + 7/2√x + 6ax  - 5a

= 15x√x/2  - 15√x/2   +  7/2√x + 6ax  - 5a

f(x)  =  √(x + a)(3x² – 5x + 7)

f'(x) =√(x + a) (6x - 5)  + (3x² – 5x + 7) /2√(x + a)

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