SOLUTION: Hi, I need to find the derivatives for the following functions:
1. f(x)=4x^5+3x^4- 8x^2+x+3
2. g(t)=t^2/5+5/t^3
3. f(x)=1.5x^2+ 2x^1.5
4. g(x)=2√x+3/√x
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Question 632025: Hi, I need to find the derivatives for the following functions:
1. f(x)=4x^5+3x^4- 8x^2+x+3
2. g(t)=t^2/5+5/t^3
3. f(x)=1.5x^2+ 2x^1.5
4. g(x)=2√x+3/√x
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
1. f(x)=4x^5+3x^4- 8x^2+x+3
f'(x)=20x^4+12x^3-16x+1
.
2. g(t)=t^2/5+5/t^3
we can rewrite as:
g(t)=(1/5)t^2+5t^(-3)
g'(t)=(2/5)t-15t^(-4)
or
g'(t)= 2t/5 -15/t^4
.
3. f(x)=1.5x^2+ 2x^1.5
f'(x)=3x+ 3x^.5
or
f'(x)=3x+ 3√x
.
4. g(x)=2√x+3/√x
we can rewrite as:
g(x)=2x^(1/2)+3/x^(1/2)
g(x)=2x^(1/2)+3x^(-1/2)
g'(x)= x^(-1/2)-(3/2)x^(-3/2)
g'(x)= 1/x^(1/2)-(3/2)/x^(3/2)
or, if you want to rationalize it
g'(x)= 1/√x -(3/2)/x^(3/2)
g'(x)= √x/x -(3/2)x^(2/3)/x
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