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Mixed Calculus Review (Logarithms and exponentials) Flashcards | StudBud

Explore/Mixed Calculus Review (Logarithms and exponentials)

Mixed Calculus Review (Logarithms and exponentials)

10 terms·StudBud Administration·39 plays

Review of Derivatives involving logarithmic and exponential functions (chain rule also included) #calculus #derivatives #integrals #logarithms #exponentials

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Questions 10

Answers

1
Where's Waldo?
Lower left
Riding the horse
Middle
Upper right
2
Find dy/dx for x²+y²=5
D: dy/dx = -x/y
A: dy/dx = x/y
C: dy/dx = (5-2x)/(2y)
B: dy/dx = - y/x
3
Find the derivative: y = 3^7x + 6x²
y' = 217x +12x
y' = 7·37x +12x
y' = 7(ln3)37x +12x
y' = (ln3)217x +12x
4
Find dy/dx for y = 2^sinx
D: dy/dx = 2sinx
B: dy/dx = (cosx)(ln2)(2sinx)
C: dy/dx = (ln2)(2sinx)
A: dy/dx = (cosx)(2sinx)
5
Find the derivative: y = (x⁵ -11)⁴
y' = 4(5x4)3
y' = 5x4(x5 -11)3
y' = 4(x5 -11)3
y' = 20x4(x5 -11)3
6
Find the derivative: y = ln(3x² + 5x - 2)
y' = (6x + 5)
y' = ln(6x + 5)
y' = (6x + 5)/(3x2 + 5x - 2)
y' = (3x2 + 5x - 2)/(6x + 5)
7
Find the derivative: y = log₃ (2x² + 3)
y' = (2x2 + 4x - 3)/[(2x2 + 3)(x + 1)]
y' = (-2x2 + x - 2)/[(2x2 +
y' = (4x)/[ln3(2x2 + 3)]
y' = (-2x2 + x - 2)/[ln3(2x2 + 3)(x + 1)]
8
Find the derivative: y = 2^x · 5x⁴
y' = 2x·20x3 + 2x·5x4
y' = (ln 2)2x·20x3
y' = 2x·20x3 - (ln5)2x·5x4
y' = 2x·20x3 + (ln2)2x·5x4
9
Find the derivative: y = 2^x· ln x
y' = 2xlnx + (ln2)2xlnx
y' = 2x/x + (ln2)2xlnx
y' = (ln 2)2x / x
y' = 2x/x + 2xlnx
10
Find the derivative: y = e^{5x - 11}
y' = 5e5x - 11
y' = e5x - 11
y' = (ln5)e5x - 11
y' = e5