7.3 Derivatives & Integrals of Logs & Exponentials

Find the derivative:
y=e^5x

• y'=e^5x
• y'=5e^5x
• y'=5e^x
• y'=(1/5)e^5x

Find the derivative:
y=4e^x²

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

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)

Find the derivative:
y=4^x

• y′=4^x
• y′=(lnx)4^x
• y′=(ln4)4^x
• y′=(log4)4^x

Find the derivative:
y=5^7x

• y′=35(ln5)5^7x
• y′=7(ln5)5^7x
• y′=5(ln7)5^7x
• y′=35(ln7)5^7x

Find the derivative:
y=11^x²

• y′=11^x²(2x)(ln11)
• y′=2x(ln11)
• y′=11^x²(2x)(lnx)
• y′=11^x²(x)(ln11)

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=log₈(3x)

• y′=1/x
• y′=1/((ln8)x)
• y′=1/(ln8)
• y′=1/((ln3)x)

Evaluate:
∫ 8e^4x dx

• (8e^4x+1)/(4x+1) +c
• 2e^4x+c
• ¼ e^4x+c
• 8e^4x+c

Evaluate:
∫ x e^-3x² dx

• -⅙ e^-3x²+c
• ⅓ e^-3x²+c
• -⅓ e^-3x²+c
• ⅙ e^-3x²+c