Exponential and Logarithmic Differentiation

What is the derivative of e^x?

• xe^x-1
• x^e
• e^x
• e^x-1

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

What is the derivative of ln(x)?

• xln(x)
• 1/x
• e^x
• ln(x+1)

Derive y=e^3x

• e^3x
• 3e^3x
• 3x
• 3xe^3x

Find dy/dx

• A

• B

• C

• D

• 1/(2x⁵)
• 1/(10x⁴)
• 2x⁵
• 5/x

Write in logarithmic form.
5² = 25

• log₅2 = 25
• log₂25 = 5
• log₂₅5 = 2
• log₅25 = 2

Write in exponential form.
log₂32 = 5

• 2^-5 = 32
• 2³² = 5
• 2⁵ = 32
• 32⁵ = 2

Simplify the expression
log(30)-log(6)

• -6log(30)
• log(24)
• log(-24)
• log(5)

Write as a single log: log 12 + 2 log x

• log (12 + 2x)
• log (14x)
• log (24x)
• log (12x²)