Derivatives of Logs and Exponentials

Find the derivative:

y=log₉x

• y′=1 /((log9)x)

• y′=(ln9)/x

• y′=1/(x(lnx))

• y′=1/((ln9)x)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Find the derivative:

y=(2^3x+4)

• 3(ln2)(2^3x+4)

• 3(2^3x+4)

• 3(2^3x+4/(ln2))

• 2^3x+4

Tags

CCSS.HSF.BF.B.5

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

Tags

CCSS.HSF.IF.A.2

CCSS.HSF.IF.C.8

Find the derivative:

y=log₄(6x+5))

• (ln4)(1/(6x+5))

• (6ln4)/(6x+5)

• 6/((ln4)(6x+5))

• 6/(6x+5)

Tags

CCSS.HSF.BF.B.5

Find the derivative:
y=4e^x²

• y'=8xe^x
• y'=8xe^x²
• y'=8xe^2x
• y'=8xe^4x²

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Find the derivative:

y=e^5x+ln(x)

• e^5+1/x

• e^5x+ln(x)

• (5+1/x) e^5x+ln(x)

• (5/x) e^5x+ln(x)

Tags

CCSS.HSF.BF.B.5

Find the derivative:
y = 3ln(x²-3)

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

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Find the derivative:

y=ln(3x²-5x)

• (6x-5)/(3x²-5)

• 6x-5

• (x³/3)-(5x²)/2

• (6x-5)/(3x³-2x)

• 1/(3x²+5)^1/4
• (3x)/(2(3x²+5))
• (2(3x²+5)^3/4)/(3x)
• (3x²+5)^1/4

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)