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Find the derivative of

You can treat
y as a composite function of
x:

so use the chain rule to differentiate
y:

The first derivative is
1/u, and the second one can be evaluated by applying the quotient rule:

Multiply out those terms in parentheses:

Substitute back for


Simplifying that product, you get

∴

I hope this helps. =)
Tags: <em>derivative composite function logarithmic logarithm log trigonometric trig secant tangent sec tan chain rule quotient rule differential integral calculus</em>
Option C would be the correct answer :)
Answer:
Time t = 2 seconds
It will reach the maximum height after 2 seconds
Completed question;
Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height, in meters above the ground, after t seconds that Amir has thrown the ball is given by:
H (t) = -(t-2)^2+9
many seconds after being thrown will the ball reach its maximum height?
Step-by-step explanation:
The equation of the height!
h(t) = -(t-2)^2 + 9 = -(t^2 -4t +4) + 9
h(t) = -t^2 +4t -4+9
h(t) = -t^2 + 4t +5
The maximum height is at dh/dt = 0
dh/dt = -2t +4 = 0
2t = 4
t = 4/2 = 2
Time t = 2 seconds
It will reach the maximum height after 2 seconds