SOLUTION: Differentiate each function. Simplify all answers, with positive exponents, and with radical notation, where possible. Questions b and d must be in simplified factored form.
a) y=
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Question 199632: Differentiate each function. Simplify all answers, with positive exponents, and with radical notation, where possible. Questions b and d must be in simplified factored form.
a) y=(4x^5)-(3x^2)+(x/5)+2pi
b) f(x)=(√x^4+2x^3-8)
c) f(x)=(4(x^2)^3/2)-(8(x^3)^3/2)/2
d) y=(2x-5)^4/(x+1)^3
e) y=[x^2+(2x+1)^3]^5
f) y=(√x-1)(x+1)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
For a) use  = x^n \ \ \Rightarrow\ \ f'(x) = nx^{n-1})
and the fact that the derivative of the sum is the sum of the derivatives.
For b) do the same thing, but realize that ^4 = x^2)
For c) remember that ^m = a^{nm})
and then use the same process as for a)
For d) use the quotient rule:
If  = \frac{g(x)}{h(x)})
where both )
and )
are differentiable and  \neq 0)
then  = \frac{g'(x)h(x)-g(x)h'(x)}{\left(h(x)\right)^2)
For e) use the chain rule:
But you will need to apply it twice working from the inside out.
For f) use the product rule:
=g(x)h(x) \ \ \Rightarrow\ \ f'(x) = g'(x)h(x)+g(x)h'(x))
If you want me to actually do these for you, write back and we'll talk.
John
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