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Question
Please I urgently need help with thesse two math questions.
Differentiate:
1/3x^6(x^2-3)
5/square root(4+x)
1/2square root (3x-1)
thank you
They are: x^6(x^2 - 3)/3, 5/√(4+x), and √(3x-1)/2. Right?
x^6(x^2 - 3)/3
The first one is a product rule with f=x^6 and g=(x^2 - 3)/3.
It is known that the answer is f'(x)*g(x) + f(x)*g'(x).
It can be seen that f'(x) = 6x^5 and g'(x) = 2x/3.
5/√(4+x)
This is really 5(4+x)^(-1/2).
The derivaitve is (-1/2)(5)(4+x)^(-3/2).
Putting that back in its proper form gives -(5/(2*(x+4)^(3/2)).
√(3x-1)/2
This is really (3x-1)^(1/2)/2. The derivative is then (1/2)(3x-1)^(-1/2)(3)/2.
This works out to 3(4*(3x-1)^(1/2)).
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