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Calculus Derivatives Flashcards | StudBud
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Calculus Derivatives
Calculus Derivatives
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Answers
1
Find the derivative of g(x) = e
2sin(x)
e2sin(x)cos(x)
2e2cos(x)cos(x)
2e2sin(x)cos(x)
2e2cos(x)
2
The derivative of y = \frac{e^x}{x+1} will be y' = g(x)/(x+1)² where g(x) is...
(x+1)e^x + e^x
(x+1)e^x - e^x
e^x - (x+1)e^x
(x+1)e^x - xe^x
3
Find the derivative of h\left(x\right)=\sqrt{7}
71/2
\frac{1}{2}\left(7\right)^{-\frac{1}{2}}
\frac{1}{2}\left(7\right)^{\frac{1}{2}}
0
4
Find dy/dx given y = tan(x) + e
x
csc2(x) + xex-1
cot(x) + ex
sec2(x) + xex-1
sec2(x) + ex
5
Last Q.: Suppose the line tangent to
f
at
x = 5
has a slope of 2. Given
f(5)
= 6, what's the equation for the line?
y = 2(x + 5) + 6
y - 5 = 2(x - 6)
y = 2x + 6
y - 6 = 2(x - 5)
6
True or False: \frac{d}{dx}\left(f\left(x\right)g\left(x\right)\right)=f'\left(x\right)g'\left(x\right)
False
True
7
State the derivative of y = f(g(2x))
y' = f'(g(2x))g'(2x)·2
y' = f'(g(2x))·2
y' = f'(g(2x))g'(2x)
y' = f'(g'(2x))
8
Find k'(4) given k(x) = ln(2x)
1/2
ln(8)
1/8
1/4
9
Given a function f(x), the formula for f'(x) is lim
t→x
of what expression?
( f(t) - f(x) ) / (t - x)
( f(t) - f(x) ) / x
( f(t) - f(x) ) / t
( f(t + x) - f(x) ) / (t - x)
10
If s(t) represents the position of an object, which of the following gives its velocity?
d2s/dt2
ds/dt
|ds/dt|
d3s/dt3
11
Find the second derivative of y = x
6
y'' = 30x4
y'' = 30x5
y'' = 30
y'' = 30x
12
True or False: The output of
f'(x)
at
x=a
is the slope of the line tangent to
f at x=a,
assuming
f
is differentiable.
True
False
