Exponential and Logarithmic Differentiation and Integration

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 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

Find the derivative:

y=log₄(6x+5))

• (ln4)(1/(6x+5))

• (6ln4)/(6x+5)

• 6/((ln4)(6x+5))

• 6/(6x+5)

Find the derivative:
y=4e^x²

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

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)

Find the derivative:

y=ln(3x²-5x)

• (6x-5)/(3x²-5)

• 6x-5

• (x³/3)-(5x²)/2

• (6x-5)/(3x³-2x)

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 f(x) = x²/e^x

• f'(x) = (x²e^x - 2xe^x) / (e^x)²
• f'(x) = (2xe^x + x²e^x) / (e^x)²
• f'(x) = (2xe^x - x²e^x) / (e^x)²
• f'(x) = x²e^x + 2xe^x