Basic Skills Jeopardy - Chapter II

Derivative Shortcuts

100

Find the derivative of x².

2x

200

Find the derivative of e^x.

e^x

300

Find the derivative of sec(x).

tan(x)sec(x)

400

Find the derivative of arctan(x).

(1)/(1+x²)

500

Find the derivative of 2^x.

2^{x *} ln(2)

Product/Quotient Rule

100

Find the derivative of x²sin(x).

2x*sin(x) + x²cos(x)

200

Find the derivative of x²/sin(x).

(2x*sin(x)-x²*cos(x))/(sin²(x))

300

Find the derivative of sec(x)x.

xsec(x)tan(x) + sec(x)

400

Find the derivative of ln(x)/tan^-1(x).

((1/x)tan^-1(x)-ln(x)(1/(1+x²)))/(tan^-1(x)²)

500

Find the derivative of ln(x)e^xcos(x)/x².

((1/x)e^xcos(x)x²+ln(x)e^xcos(x)x²-ln(x)e^xsin(x)x²-2xln(x)e^xcos(x))/(x⁴)

Chain Rule

100

Find the derivative of e^2x.

2e^2x

200

Find the derivative of sin(e^x).

e^xcos(e^x)

300

Find the derivative of (sin(x)+cos(x))².

2(cos(x)-sin(x))(sin(x)+cos(x))

400

Find the derivative of e^sin(ln(x)).

cos(ln(x))e^sin(ln(x))/x

500

Find the derivative of (x²+1)²+sin(x²+1)+ln(x²+1).

2x*(2(x²+1)+cos(x²+1)+1/(x²+1))

Implicit Differentiation

100

Find dy/dx for x²+y=1.

dy/dx = -2x

300

Find dy/dx for xy=2.

(2-y)/x

500

Find dy/dx of x²y-y=1.

(1-2xy)/(x²-1)

Antiderivatives

100

Antiderivative of x.

x²​​​​

200

Antiderivative of sin(x)

-cos(x)

300

Antiderivative of x²

x³/3

400

Antiderivative of 1/(1+x²).

arctan(x)

500

Antiderivative of x²cos(x) 2xsin(x).

x²sin(x)