Question

Find the differentiation of the following function
a) y=5x^4(x-7)^1/2
b) y=(2(x)^1/2-(3))/(x)^1/2+1

Answer 1

Use the product rule for the first and the quotient rule for the second.

1.
y = (5x^4)(x - 7)^(1/2)
dy/dx = (5x^4)(1/2)(x-7)^(-1/2) + 20x^4 (x-7)^(1/2)
I found most students find the difficulty not in finding that first derivative line, but rather in simplifying it
I don't know how far you are expected to take this "first line" derivative.
Let me know before I continue.

Answer 2

For me to simplify the answer is the most difficult. Especially when meet fraction or with surd..

Answer 3

look for common factors first,
looking at the 5x^4 and 20x^3 , that would be 5x^3
looking at the (x-7)^(-1/2) and (x-7)^(1/2) , that would be (x-7)^(-1/2) , (take the lower exponent one)
also I would take out the fraction of 1/2

= (1/2)(5x^3)(x-7)^(-1/2) [x + (2/1)(4)(x-7) ]
= (5/2)x^3 (x-7)^(-1/2) [ x + 8x - 56]
= 5x^3 (9x - 56)/(2√(x-7) )

Answer 4

How you get (2/1) in the []?