AP Calculus- log and e

Find the derivative:

y=log₉x

• y′=1 /((log9)x)

• y′=(ln9)/x

• y′=1/(x(lnx))

• y′=1/((ln9)x)

Find the derivative:

y=(2^3x+4)

• 3(ln2)(2^3x+4)

• 3(2^3x+4)

• 3(2^3x+4/(ln2))

• 2^3x+4

Find the derivative:

y=log₄(6x+5))

• (ln4)(1/(6x+5))

• (6ln4)/(6x+5)

• 6/((ln4)(6x+5))

• 6/(6x+5)

Evaluate the integral: ∫ (1/x) dx, on the interval (e, 4e).

• ln 3e

• ln 4

• -3/4e

• ln 3

• None of these

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

Find the derivative:
y = 3ln(x²-3)

• 6x/(x²-3)
• 3/(x²-3)
• 3x/(x²-3)
• 9x/(x²-3)

Find the derivative:
y = e^2x-1

• 2xe^2x-1
• e^2x-1
• 2e^2x-1
• 4e^2x-1

Tags

CCSS.HSF-IF.C.8B

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing

Tags

CCSS.HSF.IF.B.4

What is the derivative of e^x?

• xe^x-1
• x^e
• e^x
• e^x-1

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2