Welcome to the Calculus Edition of Jeopardy! (By: Rachael A. and Yuna)

Derivative of log

100

y=log₂(3x²)

What is y'=2/(xln2)

200

y=log₄x²

What is y'=1/(xln2)

300

y=log₂(3x²)

What is y'=2/(xln2)

400

y=log₅(x-7)

What is y'=1/((x-7)ln5)

500

3^xlogx=y

What is y'= 3^x*ln3*logx + 3^x/(xln10)

Derivative of ln

100

y=ln4x

What is y'= 1/x

200

y=ln(lnx)

What is y'= 1/(xlnx)

300

y=x+lnx²

What is y'= (x+2)/x

400

y=ln(sinx)

What is y'= cosx/sinx= cotx

500

y=ln(1+e^x)

What is y'=e^x/(1+e^x)

Derivative of e^x

100

y=e^2x

What is y'=2e^2x

200

y=e^-x

What is y'=-e^-x

300

y=e^(2x/3)

What is y'= (2/3)*e^(2x/3)

400

y=e^√x

What is y'= (1/(2√x))*e^√x

500

y=xe²-e^x

What is y'= e²-e^x

Derivative of a^x

100

y=3^{x^2}

What is y'=2x*3^{x^2}ln3

200

y=8^x

What is y'= 8^xln8

300

y=6^-x

What is y'=-6^-xln6

400

y=x³*8^x

What is y'= 3x²*8^x + x³*8^xln8

500

y=3^cscx

What is y'= -3^cscx*ln3*cscxcotx

Chance with Derivatives!

100

y=ln(x²)

What is y'= 2/x

200

y=log₂(x²)

What is y'= 2/(xln2)

300

y=7^x + 4e^x

What is y'= 7^xln7 + 4e^x

400

y=lnx*log₂x

What is y'= (log₂x)/x + lnx/(xln2)

500

y=x^lnx

What is y'= lnx*x^(lnx-1)*(1/x)