Derivative Rules Review Flashcards

1

Find dy/dx if y = sec(2x)

sec(2x)tan(2x)
2sec(x)tan(x)
-2sec(2x)tan(2x)
2sec(2x)tan(2x)

2

Find dy/dx for sinx+cosy = 7

sin y / cos x
-cos x / cos y
cosx-siny
-cscy * cosx

3

If y = x^π , then y' =

xπ+1/π+1
xπ *ln(x)
πxπ-1
xπ-1

4

Find f'(π) if f(x) = cos(2x)

4
0
-2
-4

5

Find the derivative of \log_{_5}4x²

\frac{2}{x\ln5}
\frac{1}{5\ln4x^2}
\frac{1}{4x^2\ln5}
\frac{1}{4x^2}

6

If f and g are differentiable functions, and H(x) = f(x)*g(x), find H'(2).

-20
-7
13
-6

7

Find dy/dx for x² + y² = 4

x/y
-x/y
-y/x
2x+2y

8

Find the derivative of y = ln(2x-7)

(2x-7)/2
2/(2x-7)
1/(2x-7)
(2x - 7)/ln(2x - 7)

9

Find the derivative of tan(4x+π)

-sec (4x+π)2
4sec2 (4x+π)
4sec(4x+π)tan(4x+π)
-sec2 (4x+π)

10

Find the derivative of y = (3x-4)¹⁰⁰

y'=100(3x-4)99
y=3(3x-4)99
y'=(3x-4)101 /101
y'=300(3x-4)99

11

Find f'(x) if f(x) = cot(x+2)

-cot(x+2)csc(x+2)
csc2 (x+2)
-csc2 (x+2)
cot(x+2)csc(x+2)

12

If f(x) =\left(\frac{2}{t}+t^5\right)\left(t^3+1\right) , then f'(x) = ?

2t^7-8t
\left(-2t^{-2}+5t^4\right)\left(3t^2\right)
8t^7+4t
15t^6

13

Write the equation of the tangent line to the function f(x)=3x² +4 at x = 3.

y - 31 = 22 (x - 3)
y - 31 = 18(x - 3)
y -31 = (1/22) (x - 3)
y - 31 = (1/18)(x - 3)

14

If f and g are differentiable functions, and H(x) = f(g(x)), find H'(1).

6
-12
4
-6

15

Find dy/dx of 2π

2π
0
2
1

16

Find the y' if y = cos(7-x)

-cos(7-x)
sin(7-x)
cos(7-x)
-sin(7-x)

17

Find the derivative of e^7x-4

y'=-7e7x-4
y'=e7
y'=7e7x-4
y'=e7x-4

18

If 𝒚=2^x , then what is dy/dx?

ln(2)
x*2x-1
2x *ln(2)
2x+1 /(x+1)

19

Find the derivative of y = sin(x)

y' = -sec x
y' = -cos x
y' = sec x
y' = cos x

Derivative Rules Review

Questions 19

Derivative Rules Review

Questions 19