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I am also on the next question, i have solved a few and struggling with others?
2. obtain dy/dx for the following functions using the 'direct rule'
a) y=2.5x^2
=5x
b) y=x^2/2.5
=0.8x
c) y=2.5x - 2.5
=-2.5x^0
d)y= (2.5)(SQUAREROOT OF x)
=1.25x
e)y=x^2.5
=2.5^1.5
f)y=2.5/x^2 HELP
g)y=(^2.5 SQUARE ROOT OF x) HELP
h)y=2.5x^4 - (x^3/2.5) - (x/2.5) + 2.5 SO FAR
=10x^3 - 1.2x^2 - 0.4x^0 + 2.5
I)y=2.5x{(x^2)-(1)} HELP
J) y=(x^3 - 2.5x^2) / (2.5) (SQUARE ROOT OF x) HELP
d)
$\displaystyle y = 2.5 \sqrt(x) = 2.5 x^{0.5} $
By the power rule
$\displaystyle y' = 0.5*2.5 x^{0.5-1} = \dfrac{1.25}{\sqrt{x}}$
f)
$\displaystyle y = \dfrac{2.5}{x^2} = 2.5 x^{-2}$ now use the power rule. [Typo Fixed]
g) What?
h) If C is a constant then $\displaystyle \frac{d}{dx}[C] = 0$
I)
$\displaystyle y=2.5 x(x^2 -1) = 2.5x^3 - 2.5x$ Now use a combination of power rule and sum rule
J)
$\displaystyle y=\dfrac{x^3 - 2.5x^2}{2.5\sqrt{ x}} = 0.4x^{2.5} - x^{1.5}$ Now use a combination of the power rule and sum rule.
Ok i have attempted the questions you have helped me with:
d) 1.25^-0.5x
f) 5x
h) 10x^3 - 1.2x - 0.4x + 2.5
I) (7.5x^2) - (2.5x)
J) (x^1.5) - (1.5x^0.5)
Thankyou
d) How did you get 1.25^-0.5x? lvleph had already given you the correct answer...
e) $\displaystyle y=x^{2.5}$
$\displaystyle \frac{dy}{dx}=2.5^{1.5}$
Where'd your x go? If it's $\displaystyle \frac{dy}{dx}=2.5x^{1.5}$ then it is correct.
f) y=2.5/x^2
Another way of writing this is $\displaystyle y=2.5x^{-2}$
g) Doesn't make sense. Is it $\displaystyle y= \sqrt{x}^{2.5})$??
h) $\displaystyle y=2.5x^4 - \frac{x^3}{2.5} - \frac{x}{2.5} + 2.5$
You are almost there. Why do you still have that + 2.5 part at the end?
i) (7.5x^2) - (2.5x)
Almost there with this one as well. You haven't seemed to have differentiated the 2.5x part yet.
j) Correct.
Typo! lvleph surely meant $\displaystyle 2.5 x^{-2}$Quote:
Originally Posted by lvleph
Quote:
g) What?
h) If C is a constant then $\displaystyle \frac{d}{dx}[C] = 0$
I)
$\displaystyle y=2.5 x(x^2 -1) = 2.5x^3 - 2.5x$ Now use a combination of power rule and sum rule
J)
$\displaystyle y=\dfrac{x^3 - 2.5x^2}{2.5\sqrt{ x}} = 0.4x^{2.5} - x^{1.5}$ Now use a combination of the power rule and sum rule.
Maybe g) is $\displaystyle x^{1/2.5}$?
