Jeopardy for Derivative and Integral

Basic Derivative

100

f(x)=xⁿ

f'(x)=nx^(n-1)

200

f(x)=a^x

f'(x)=a^x.ln(a)

300

f(x)=ln(x)

f'(x)=1/x

400

f(x)=cos(x)

f'(x)=-sin(x)

500

f(x)=cos^-1(x)

f'(x)=-1/sqrt(1-x²)

Basic Integral

100

Integral of xⁿ

x⁽ⁿ⁺¹⁾/(n+1)+C

200

Integral of a^x

a^x/ln(a)+C

300

Integral of 1/x

ln|x|+C

400

Integral of sin(x)

-cos(x)+C

500

Integral of 1/sqrt(1-x²)

sin^-1(x)+C

Find the Derivative

100

f(x)=e^sqrt(x)

f'(x)=e^sqrt(x)/(2sqrt(x))

200

f(x)=ln(ln(x))

f'(x)=1/(ln(x).x)

300

f(x)=cos⁵(3x²-7)

f'(x)=5cos⁴(3x²-7).6x

400

f(x)=tan(5x²+8)

f'(x)=sec²(5x²+8).10x

500

f(x)=tan^-1(x/3)

f'(x)=3/(9+x²)

Find the integral

100

Integral of 1/x^1/5

5/4.x^4/5+C

200

Integral of sec²(x)

tan(x)+C

300

Integral of sec(x)tan(x)

sec(x)+C

400

Integral of tan(x)

ln|sec(x)|+C

500

Integral of 1/(x.sqrt(x²-1))

sec^-1(x)+C